*labels=alphabetic

• Alano Ancona, Negatively curved manifolds, elliptic operators, and the Martin boundary, Ann. of Math. (2) 125 (1987), no. 3, 495–536. MR 890161, DOI 10.2307/1971409
• Michael T. Anderson and Richard Schoen, Positive harmonic functions on complete manifolds of negative curvature, Ann. of Math. (2) 121 (1985), no. 3, 429–461. MR 794369, DOI 10.2307/1971181
• D. V. Anosov, Tangential fields of transversal foliations in ${U}$-systems, Mat. Zametki 2 (1967), 539–548 (Russian). MR 242190
• D. V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature, Proceedings of the Steklov Institute of Mathematics, No. 90 (1967), American Mathematical Society, Providence, RI, 1969. Translated from the Russian by S. Feder. MR 242194
• Ludwig Arnold, Random dynamical systems, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. MR 1723992, DOI 10.1007/978-3-662-12878-7
• Viviane Baladi, Linear response, or else, Proceedings of the International Congress of Mathematicians—Seoul 2014. Vol. III, Kyung Moon Sa, Seoul, 2014, pp. 525–545. MR 3729040
• Werner Ballmann, Lectures on spaces of nonpositive curvature, DMV Seminar, vol. 25, Birkhäuser Verlag, Basel, 1995. With an appendix by Misha Brin. MR 1377265, DOI 10.1007/978-3-0348-9240-7
• Werner Ballmann, Mikhael Gromov, and Viktor Schroeder, Manifolds of nonpositive curvature, Progress in Mathematics, vol. 61, Birkhäuser Boston, Inc., Boston, MA, 1985. MR 823981, DOI 10.1007/978-1-4684-9159-3
• G. Besson, G. Courtois, and S. Gallot, Entropies et rigidités des espaces localement symétriques de courbure strictement négative, Geom. Funct. Anal. 5 (1995), no. 5, 731–799 (French). MR 1354289, DOI 10.1007/BF01897050
• Yves Benoist, Patrick Foulon, and François Labourie, Flots d’Anosov à distributions stable et instable différentiables, J. Amer. Math. Soc. 5 (1992), no. 1, 33–74 (French, with English summary). MR 1124979, DOI 10.1090/S0894-0347-1992-1124979-1
• Jean-Michel Bismut, Martingales, the Malliavin calculus and Hörmander’s theorem, Stochastic integrals (Proc. Sympos., Univ. Durham, Durham, 1980) Lecture Notes in Math., vol. 851, Springer, Berlin, 1981, pp. 85–109. MR 620987
• Jean-Michel Bismut, Martingales, the Malliavin calculus and hypoellipticity under general Hörmander’s conditions, Z. Wahrsch. Verw. Gebiete 56 (1981), no. 4, 469–505. MR 621660, DOI 10.1007/BF00531428
• K. Burns and A. Katok, Manifolds with nonpositive curvature, Ergodic Theory Dynam. Systems 5 (1985), no. 2, 307–317. MR 796758, DOI 10.1017/S0143385700002935
• R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under translations, Ann. of Math. (2) 45 (1944), 386–396. MR 10346, DOI 10.2307/1969276
• R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under a general class of linear transformations, Trans. Amer. Math. Soc. 58 (1945), 184–219. MR 13240, DOI 10.1090/S0002-9947-1945-0013240-1
• A. P. Carverhill and K. D. Elworthy, Lyapunov exponents for a stochastic analogue of the geodesic flow, Trans. Amer. Math. Soc. 295 (1986), no. 1, 85–105. MR 831190, DOI 10.1090/S0002-9947-1986-0831190-1
• S. Y. Cheng and S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), no. 3, 333–354. MR 385749, DOI 10.1002/cpa.3160280303
• Gonzalo Contreras, Regularity of topological and metric entropy of hyperbolic flows, Math. Z. 210 (1992), no. 1, 97–111. MR 1161172, DOI 10.1007/BF02571785
• Kevin Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. (2) 135 (1992), no. 1, 165–182. MR 1147961, DOI 10.2307/2946567
• Bruce K. Driver, A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold, J. Funct. Anal. 110 (1992), no. 2, 272–376. MR 1194990, DOI 10.1016/0022-1236(92)90035-H
• Bruce K. Driver, A Cameron-Martin type quasi-invariance theorem for pinned Brownian motion on a compact Riemannian manifold, Trans. Amer. Math. Soc. 342 (1994), no. 1, 375–395. MR 1154540, DOI 10.1090/S0002-9947-1994-1154540-2
• Bruce K. Driver, Integration by parts for heat kernel measures revisited, J. Math. Pures Appl. (9) 76 (1997), no. 8, 703–737. MR 1470881, DOI 10.1016/S0021-7824(97)89966-7
• P. Eberlein and B. O’Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45–109. MR 336648
• K. D. Elworthy, Stochastic differential equations on manifolds, London Mathematical Society Lecture Note Series, vol. 70, Cambridge University Press, Cambridge-New York, 1982. MR 675100
• V. A. Kaĭmanovich and A. G. Èrshler, Continuity of asymptotic characteristics for random walks on hyperbolic groups, Funktsional. Anal. i Prilozhen. 47 (2013), no. 2, 84–89 (Russian); English transl., Funct. Anal. Appl. 47 (2013), no. 2, 152–156. MR 3113872, DOI 10.1007/s10688-013-0020-1
• Jost-Hinrich Eschenburg, Horospheres and the stable part of the geodesic flow, Math. Z. 153 (1977), no. 3, 237–251. MR 440605, DOI 10.1007/BF01214477
• A. Fathi and L. Flaminio, Infinitesimal conjugacies and Weil-Petersson metric, Ann. Inst. Fourier (Grenoble) 43 (1993), no. 1, 279–299 (English, with English and French summaries). MR 1209705
• Livio Flaminio, Local entropy rigidity for hyperbolic manifolds, Comm. Anal. Geom. 3 (1995), no. 3-4, 555–596. MR 1371210, DOI 10.4310/CAG.1995.v3.n4.a2
• Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1964. MR 181836
• Patrick Foulon and François Labourie, Sur les variétés compactes asymptotiquement harmoniques, Invent. Math. 109 (1992), no. 1, 97–111 (French). MR 1168367, DOI 10.1007/BF01232020
• A. Freire and R. Mañé, On the entropy of the geodesic flow in manifolds without conjugate points, Invent. Math. 69 (1982), no. 3, 375–392. MR 679763, DOI 10.1007/BF01389360
• Sylvestre Gallot, Dominique Hulin, and Jacques Lafontaine, Riemannian geometry, 3rd ed., Universitext, Springer-Verlag, Berlin, 2004. MR 2088027, DOI 10.1007/978-3-642-18855-8
• Lucy Garnett, Foliations, the ergodic theorem and Brownian motion, J. Functional Analysis 51 (1983), no. 3, 285–311. MR 703080, DOI 10.1016/0022-1236(83)90015-0
• I. V. Girsanov, On transforming a class of stochastic processes by absolutely continuous substitution of measures, Teor. Verojatnost. i Primenen. 5 (1960), 314–330 (Russian, with English summary). MR 133152
• Sébastien Gouëzel, Analyticity of the entropy and the escape rate of random walks in hyperbolic groups, Discrete Anal. , posted on (2017), Paper No. 7, 37. MR 3651925, DOI 10.19086/da.1639
• Sébastien Gouëzel, Frédéric Mathéus, and François Maucourant, Entropy and drift in word hyperbolic groups, Invent. Math. 211 (2018), no. 3, 1201–1255. MR 3763407, DOI 10.1007/s00222-018-0788-y
• Alexander Grigor’yan, Heat kernel and analysis on manifolds, AMS/IP Studies in Advanced Mathematics, vol. 47, American Mathematical Society, Providence, RI; International Press, Boston, MA, 2009. MR 2569498, DOI 10.1090/amsip/047
• Alexander Grigor′yan, Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds, Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 2, 135–249. MR 1659871, DOI 10.1090/S0273-0979-99-00776-4
• Mikhael Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983), no. 1, 1–147. MR 697984
• Y. Guivarc’h, Sur la loi des grands nombres et le rayon spectral d’une marche aléatoire, Conference on Random Walks (Kleebach, 1979) Astérisque, vol. 74, Soc. Math. France, Paris, 1980, pp. 47–98, 3 (French, with English summary). MR 588157
• Richard S. Hamilton, A matrix Harnack estimate for the heat equation, Comm. Anal. Geom. 1 (1993), no. 1, 113–126. MR 1230276, DOI 10.4310/CAG.1993.v1.n1.a6
• Ursula Hamenstädt, An explicit description of harmonic measure, Math. Z. 205 (1990), no. 2, 287–299. MR 1076134, DOI 10.1007/BF02571241
• Ernst Heintze and Hans-Christoph Im Hof, Geometry of horospheres, J. Differential Geometry 12 (1977), no. 4, 481–491 (1978). MR 512919
• Elton P. Hsu, Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold, J. Funct. Anal. 134 (1995), no. 2, 417–450. MR 1363807, DOI 10.1006/jfan.1995.1152
• Elton P. Hsu, Estimates of derivatives of the heat kernel on a compact Riemannian manifold, Proc. Amer. Math. Soc. 127 (1999), no. 12, 3739–3744. MR 1618694, DOI 10.1090/S0002-9939-99-04967-9
• Elton P. Hsu, Stochastic analysis on manifolds, Graduate Studies in Mathematics, vol. 38, American Mathematical Society, Providence, RI, 2002. MR 1882015, DOI 10.1090/gsm/038
• Nobuyuki Ikeda and Shinzo Watanabe, Stochastic differential equations and diffusion processes, 2nd ed., North-Holland Mathematical Library, vol. 24, North-Holland Publishing Co., Amsterdam; Kodansha, Ltd., Tokyo, 1989. MR 1011252
• A. Katok, Entropy and closed geodesics, Ergodic Theory Dynam. Systems 2 (1982), no. 3-4, 339–365 (1983). MR 721728, DOI 10.1017/S0143385700001656
• Anatole Katok, Nonuniform hyperbolicity and structure of smooth dynamical systems, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 1245–1253. MR 804774
• A. Katok, G. Knieper, M. Pollicott, and H. Weiss, Differentiability and analyticity of topological entropy for Anosov and geodesic flows, Invent. Math. 98 (1989), no. 3, 581–597. MR 1022308, DOI 10.1007/BF01393838
• Anatole Katok, Gerhard Knieper, and Howard Weiss, Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows, Comm. Math. Phys. 138 (1991), no. 1, 19–31. MR 1108034
• Gerhard Knieper and Howard Weiss, Regularity of measure theoretic entropy for geodesic flows of negative curvature. I, Invent. Math. 95 (1989), no. 3, 579–589. MR 979366, DOI 10.1007/BF01393891
• V. A. Kaĭmanovich, Brownian motion and harmonic functions on covering manifolds. An entropic approach, Dokl. Akad. Nauk SSSR 288 (1986), no. 5, 1045–1049 (Russian). MR 852647
• Vadim A. Kaimanovich, Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds, Ann. Inst. H. Poincaré Phys. Théor. 53 (1990), no. 4, 361–393 (English, with French summary). Hyperbolic behaviour of dynamical systems (Paris, 1990). MR 1096098
• Tosio Kato, Perturbation theory for linear operators, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1980 edition. MR 1335452
• Gerhard Knieper, A second derivative formula of the Liouville entropy at spaces of constant negative curvature, Ergodic Theory Dynam. Systems 17 (1997), no. 5, 1131–1135. MR 1477035, DOI 10.1017/S0143385797086446
• Hiroshi Kunita, Stochastic flows and stochastic differential equations, Cambridge Studies in Advanced Mathematics, vol. 24, Cambridge University Press, Cambridge, 1990. MR 1070361
• André Lichnerowicz, Sur les espaces riemanniens complètement harmoniques, Bull. Soc. Math. France 72 (1944), 146–168 (French). MR 12886
• F. Ledrappier, Ergodic properties of Brownian motion on covers of compact negatively-curve manifolds, Bol. Soc. Brasil. Mat. 19 (1988), no. 1, 115–140. MR 1018929, DOI 10.1007/BF02584822
• F. Ledrappier, Harmonic measures and Bowen-Margulis measures, Israel J. Math. 71 (1990), no. 3, 275–287. MR 1088820, DOI 10.1007/BF02773746
• François Ledrappier, Central limit theorem in negative curvature, Ann. Probab. 23 (1995), no. 3, 1219–1233. MR 1349169
• François Ledrappier, Linear drift and entropy for regular covers, Geom. Funct. Anal. 20 (2010), no. 3, 710–725. MR 2720229, DOI 10.1007/s00039-010-0080-9
• François Ledrappier, Regularity of the entropy for random walks on hyperbolic groups, Ann. Probab. 41 (2013), no. 5, 3582–3605. MR 3127892, DOI 10.1214/12-AOP748
• François Ledrappier and Lin Shu, Entropy rigidity of symmetric spaces without focal points, Trans. Amer. Math. Soc. 366 (2014), no. 7, 3805–3820. MR 3192619, DOI 10.1090/S0002-9947-2014-06016-9
• François Ledrappier and Lin Shu, Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes, Ann. Inst. Fourier (Grenoble) 67 (2017), no. 3, 1115–1183 (English, with English and French summaries). MR 3668769
• Xiang-Dong Li, Hamilton’s Harnack inequality and the $W$-entropy formula on complete Riemannian manifolds, Stochastic Process. Appl. 126 (2016), no. 4, 1264–1283. MR 3461198, DOI 10.1016/j.spa.2015.11.002
• R. de la Llave, J. M. Marco, and R. Moriyón, Canonical perturbation theory of Anosov systems and regularity results for the Livšic cohomology equation, Ann. of Math. (2) 123 (1986), no. 3, 537–611. MR 840722, DOI 10.2307/1971334
• Xiaonan Ma and George Marinescu, Exponential estimate for the asymptotics of Bergman kernels, Math. Ann. 362 (2015), no. 3-4, 1327–1347. MR 3368102, DOI 10.1007/s00208-014-1137-0
• Paul Malliavin, Stochastic calculus of variation and hypoelliptic operators, Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976) Wiley-Intersci. Publ., John Wiley & Sons, New York-Chichester-Brisbane, 1978, pp. 195–263. MR 536013
• Paul Malliavin, Stochastic Jacobi fields, Partial differential equations and geometry (Proc. Conf., Park City, Utah, 1977) Lect. Notes Pure Appl. Math., vol. 48, Dekker, New York, 1979, pp. 203–235. MR 535595
• Paul Malliavin, $C^{k}$-hypoellipticity with degeneracy, Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1978) Academic Press, New York-London, 1978, pp. 199–214. MR 517243
• Paul Malliavin, $C^{k}$-hypoellipticity with degeneracy. II, Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1978) Academic Press, New York-London, 1978, pp. 327–340. MR 517250
• Paul Malliavin, Stochastic analysis, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 313, Springer-Verlag, Berlin, 1997. MR 1450093, DOI 10.1007/978-3-642-15074-6
• Anthony Manning, Topological entropy for geodesic flows, Ann. of Math. (2) 110 (1979), no. 3, 567–573. MR 554385, DOI 10.2307/1971239
• Anthony Manning, The volume entropy of a surface decreases along the Ricci flow, Ergodic Theory Dynam. Systems 24 (2004), no. 1, 171–176. MR 2041266, DOI 10.1017/S0143385703000415
• P. Mathieu, Differentiating the entropy of random walks on hyperbolic groups, Ann. Probab. 43 (2015), no. 1, 166–187. MR 3298471, DOI 10.1214/13-AOP901
• M. Misiurewicz, On non-continuity of topological entropy, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 19 (1971), 319–320 (English, with Russian summary). MR 287578
• M. Misiurewicz, Diffeomorphism without any measure with maximal entropy, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 21 (1973), 903–910 (English, with Russian summary). MR 336764
• G. D. Mostow, Quasi-conformal mappings in $n$-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 53–104. MR 236383
• Sheldon E. Newhouse, Continuity properties of entropy, Ann. of Math. (2) 129 (1989), no. 2, 215–235. MR 986792, DOI 10.2307/1971492
• A. A. Novikov, On moment inequalities and identities for stochastic integrals, Proceedings of the Second Japan-USSR Symposium on Probability Theory (Kyoto, 1972) Lecture Notes in Math., Vol. 330, Springer, Berlin-New York, 1973, pp. 333–339. MR 448553
• Mark A. Pinsky, Isotropic transport process on a Riemannian manifold, Trans. Amer. Math. Soc. 218 (1976), 353–360. MR 402957, DOI 10.1090/S0002-9947-1976-0402957-2
• M. Pollicott, Analyticity of dimensions for hyperbolic surface diffeomorphisms, Proc. Amer. Math. Soc. 143 (2015), no. 8, 3465–3474. MR 3348789, DOI 10.1090/proc/12477
• Daniel Revuz and Marc Yor, Continuous martingales and Brownian motion, 3rd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 293, Springer-Verlag, Berlin, 1999. MR 1725357, DOI 10.1007/978-3-662-06400-9
• Steven Rosenberg, The Laplacian on a Riemannian manifold, London Mathematical Society Student Texts, vol. 31, Cambridge University Press, Cambridge, 1997. An introduction to analysis on manifolds. MR 1462892, DOI 10.1017/CBO9780511623783
• David Ruelle, Differentiation of SRB states, Comm. Math. Phys. 187 (1997), no. 1, 227–241. MR 1463827, DOI 10.1007/s002200050134
• David Ruelle, General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium, Phys. Lett. A 245 (1998), no. 3-4, 220–224. MR 1642617, DOI 10.1016/S0375-9601(98)00419-8
• David Ruelle, Differentiating the absolutely continuous invariant measure of an interval map $f$ with respect to $f$, Comm. Math. Phys. 258 (2005), no. 2, 445–453. MR 2171702, DOI 10.1007/s00220-004-1267-4
• David Ruelle, Differentiation of SRB states for hyperbolic flows, Ergodic Theory Dynam. Systems 28 (2008), no. 2, 613–631. MR 2408395, DOI 10.1017/S0143385707000260
• David Ruelle, A review of linear response theory for general differentiable dynamical systems, Nonlinearity 22 (2009), no. 4, 855–870. MR 2486360, DOI 10.1088/0951-7715/22/4/009
• Hans Henrik Rugh, On the dimensions of conformal repellers. Randomness and parameter dependency, Ann. of Math. (2) 168 (2008), no. 3, 695–748. MR 2456882, DOI 10.4007/annals.2008.168.695
• Laurent Saloff-Coste, Uniformly elliptic operators on Riemannian manifolds, J. Differential Geom. 36 (1992), no. 2, 417–450. MR 1180389
• Yum Tong Siu, The complex-analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. of Math. (2) 112 (1980), no. 1, 73–111. MR 584075, DOI 10.2307/1971321
• Michael Shub, Global stability of dynamical systems, Springer-Verlag, New York, 1987. With the collaboration of Albert Fathi and Rémi Langevin; Translated from the French by Joseph Christy. MR 869255, DOI 10.1007/978-1-4757-1947-5
• A. V. Skorohod, A note on Gaussian measures in Banach space, Teor. Verojatnost. i Primenen. 15 (1970), 519–520 (Russian, with English summary). MR 277684
• Michael Spivak, A comprehensive introduction to differential geometry. Vol. II, 2nd ed., Publish or Perish, Inc., Wilmington, DE, 1979. MR 532831
• Daniel W. Stroock and James Turetsky, Upper bounds on derivatives of the logarithm of the heat kernel, Comm. Anal. Geom. 6 (1998), no. 4, 669–685. MR 1664888, DOI 10.4310/CAG.1998.v6.n4.a2
• W. P. Thurston, The geometry and topology of three-manifolds, Electronic version 1.1, 2002.
• Shinzo Watanabe, Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels, Ann. Probab. 15 (1987), no. 1, 1–39. MR 877589
• Shing Tung Yau, On the heat kernel of a complete Riemannian manifold, J. Math. Pures Appl. (9) 57 (1978), no. 2, 191–201. MR 505904
• Y. Yomdin, Volume growth and entropy, Israel J. Math. 57 (1987), no. 3, 285–300. MR 889979, DOI 10.1007/BF02766215
• Y. Yomdin, $C^k$-resolution of semialgebraic mappings. Addendum to: “Volume growth and entropy”, Israel J. Math. 57 (1987), no. 3, 301–317. MR 889980, DOI 10.1007/BF02766216

*labels=alphabetic

• Alano Ancona, Negatively curved manifolds, elliptic operators, and the Martin boundary, Ann. of Math. (2) 125 (1987), no. 3, 495–536. MR 890161
• Michael T. Anderson and Richard Schoen, Positive harmonic functions on complete manifolds of negative curvature, Ann. of Math. (2) 121 (1985), no. 3, 429–461. MR 794369
• D. V. Anosov, Tangent fields of transversal foliations in U-systems, Mathematical notes of the Academy of Sciences of the USSR 2 (1967), 818–823. MR 0242190 (39 \#3523)
• D. V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature. , Proceedings of the Steklov Institute of Mathematics, No. 90 (1967). Translated from the Russian by S. Feder, American Mathematical Society, Providence, R.I., 1969. MR 0242194
• Ludwig Arnold, Random dynamical systems, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. MR 1723992
• Viviane Baladi, Linear response, or else, Proceedings of the International Congress of Mathematicians—Seoul 2014. Vol. III, Kyung Moon Sa, Seoul, 2014, pp. 525–545. MR 3729040
• W. Ballmann, Lectures on spaces of nonpositive curvature. With an appendix by Misha Brin, DMV Seminar, 25, Birkhäuser Verlag, Basel, 1995. MR 1377265 (97a:53053)
• W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of nonpositive curvature, Progress in Mathematics, 61, Birkhäuser Boston, Inc., Boston, MA, 1985. MR 0823981 (87h:53050)
• G. Besson, G. Courtois, and S. Gallot, Entropies et rigidités des espaces localement symétriques de courbure strictement négative, Geom. Funct. Anal. 5 (1995), no. 3, 731–799. MR 1354289 (96i:58136)
• Y. Benoist, P. Foulon, and F. Labourie, Flots d’Anosov à distributions stables et instables différentiables, J. Amer. Math. Soc. 5 (1992), no. 1, 33–74. MR 1124979 (93b:58112)
• Jean-Michel Bismut, Martingales, the Malliavin calculus and Hörmander’s theorem, Stochastic integrals (Proc. Sympos., Univ. Durham, Durham, 1980) Lecture Notes in Math., vol. 851, Springer, Berlin, 1981, pp. 85–109. MR 620987
• J.-M. Bismut, Martingales, the Malliavin calculus and hypoellipticity under general Hörmander’s conditions, Z. Wahrsch. Verw. Gebiete 56 (1981), no. 4, 469–505. MR 0621660 (82k:60134)
• K. Burns and A. Katok, Manifolds with nonpositive curvature, Ergodic Theory Dynam. Systems 5 (1985), no. 2, 307–317. MR 0796758 (86j:53060)
• R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under translations, Ann. of Math. (2) 45 (1944), 386–396. MR 0010346 (6,5f)
• R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under a general class of linear transformations, Trans. Amer. Math. Soc. 58 (1945), 184–219. MR 13240
• A. P. Carverhill and K. D. Elworthy, Lyapunov exponents for a stochastic analogue of the geodesic flow, Trans. Amer. Math. Soc. 295 (1986), no. 1, 85–105. MR 831190
• S. Y. Cheng and S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), no. 3, 333–354. MR 0385749 (52 \#6608)
• G. Contreras, Regularity of topological and metric entropy of hyperbolic flows, Math. Z. 210 (1992), no. 1, 97–111. MR 1161172 (93f:58179)
• K. Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. (2) 135 (1992), no. 1, 165–182. MR 1147961 (92m:57048)
• Bruce K. Driver, A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold, J. Funct. Anal. 110 (1992), no. 2, 272–376. MR 1194990
• Bruce K. Driver, A Cameron-Martin type quasi-invariance theorem for pinned Brownian motion on a compact Riemannian manifold, Trans. Amer. Math. Soc. 342 (1994), no. 1, 375–395. MR 1154540
• Bruce K. Driver, Integration by parts for heat kernel measures revisited, J. Math. Pures Appl. (9) 76 (1997), no. 8, 703–737. MR 1470881
• P. Eberlein and B. O’Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45–109. MR 0336648 (49 \#1421)
• K. D. Elworthy, Stochastic differential equations on manifolds, London Mathematical Society Lecture Note Series, 70, Cambridge University Press, Cambridge-New York, 1982. MR 675100 (84d:58080)
• A. G. Ershler and V. A. Kaimanovich, Continuity of asymptotic characteristics for random walks on hyperbolic groups, Funct. Anal. Appl. 47 (2013), no. 2, 152–156. (English translation of Funktsional. Anal. i Prilozhen. 47 (2013), no. 2, 84–89.). MR 3113872
• Jost-Hinrich Eschenburg, Horospheres and the stable part of the geodesic flow, Math. Z. 153 (1977), no. 3, 237–251. MR 440605
• A. Fathi and L. Flaminio, Infinitesimal conjugacies and Weil-Petersson metric, Ann. Inst. Fourier (Grenoble) 43 (1993), no. 1, 279–299. MR 1209705 (94c:58149)
• Livio Flaminio, Local entropy rigidity for hyperbolic manifolds, Comm. Anal. Geom. 3 (1995), no. 3-4, 555–596. MR 1371210
• Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0181836
• P. Foulon and F. Labourie, Sur les variétés compactes asymptotiquement harmoniques, Invent. Math. 109 (1992), no. 1, 97–111. MR 1168367 (93g:58114)
• A. Freire and R. Mañé, On the entropy of the geodesic flow in manifolds without conjugate points, Invent. Math. 69 (1982), no. 3, 375–392. MR 0679763 (84d:58063)
• S. Gallot, D. Hulin, and J. Lafontaine, Riemannian geometry, Universitext, Springer, Berlin, Heidelberg, 2004. Third edition. MR 2088027 (2005e:53001)
• L. Garnett, Foliations, the ergodic theorem and Brownian motion, J. Funct. Anal. 51 (1983), no. 3, 285–311. MR 0703080 (84j:58099)
• I. V. Girsanov, On transforming a class of stochastic processes by absolutely continuous substitution of measures, Teor. Verojatnost. i Primenen. 5 (1960), 314–330 (Russian, with English summary). MR 0133152
• S. Gouëzel, Analyticity of the entropy and the escape rate of random walks in hyperbolic groups, Discrete Anal. 7 (2017), 37pp. MR 3651925
• S. Gouëzel, F. Mathéus, and F. Maucourant, Entropy and drift in word hyperbolic groups, Invent. Math. 211 (2018), no. 3, 1201–1255. MR 3763407
• Alexander Grigor’yan, Heat kernel and analysis on manifolds, AMS/IP Studies in Advanced Mathematics, vol. 47, American Mathematical Society, Providence, RI; International Press, Boston, MA, 2009. MR 2569498
• Alexander Grigor′yan, Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds, Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 2, 135–249. MR 1659871
• M. Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983), no. 1, 1–147. MR 0697984 (85h:53029)
• Y. Guivarc’h, Sur la loi des grands nombres et le rayon spectral d’une marche aléatoire, Conference on Random Walks (Kleebach, 1979) Astérisque, vol. 74, Soc. Math. France, Paris, 1980, pp. 47–98, 3 (French, with English summary). MR 588157
• Richard S. Hamilton, A matrix Harnack estimate for the heat equation, Comm. Anal. Geom. 1 (1993), no. 1, 113–126. MR 1230276
• Ursula Hamenstädt, An explicit description of harmonic measure, Math. Z. 205 (1990), no. 2, 287–299. MR 1076134 (91k:58104)
• E. Heintze and H.-C. Im Hof, Geometry of horospheres, J. Differential Geom. 12 (1977), no. 4, 481–491 (1978). MR 512919 (80a:53051)
• Elton P. Hsu, Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold, J. Funct. Anal. 134 (1995), no. 2, 417–450. MR 1363807
• E.-P. Hsu, Estimates of derivatives of the heat kernel on a compact Riemannian manifold, Proc. Amer. Math. Soc. 127 (1999), no. 12, 3739–3744. MR 1618694 (2000c:58047)
• Elton P. Hsu, Stochastic analysis on manifolds, Graduate Studies in Mathematics, vol. 38, American Mathematical Society, Providence, RI, 2002. MR 1882015
• Nobuyuki Ikeda and Shinzo Watanabe, Stochastic differential equations and diffusion processes, 2nd ed., North-Holland Mathematical Library, vol. 24, North-Holland Publishing Co., Amsterdam; Kodansha, Ltd., Tokyo, 1989. MR 1011252
• A. Katok, Entropy and closed geodesics, Ergodic Theory Dynam. Systems 2 (1982), no. 3-4, 339–365. MR 0721728 (85b:53047)
• Anatole Katok, Nonuniform hyperbolicity and structure of smooth dynamical systems, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 1245–1253. MR 804774
• A. Katok, G. Knieper, M. Pollicott, and H. Weiss, Differentiability and analyticity of topological entropy for Anosov and geodesic flows, Invent. Math. 98 (1989), no. 3, 581–597. MR 1022308 (90i:58150)
• A. Katok, G. Knieper, and H. Weiss, Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows, Comm. Math. Phys. 138 (1991), no. 1, 19–31. MR 1108034 (92d:58162)
• G. Knieper and H. Weiss, Regularity of measure theoretic entropy for geodesic flows of negative curvature I, Invent. Math. 95 (1989), no. 3, 579–589. MR 0979366 (90e:58128)
• V. A. Kaimanovich, Brownian motion and harmonic functions on covering manifolds. An entropic approach, Soviet Math. Dokl 33 (1986), 812–816. (English translation of Dokl. Akad. Nauk SSSR 288 (1986), no. 5, 1045–1049.) MR 0852647 (88k:58163)
• Vadim A. Kaimanovich, Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds, Ann. Inst. H. Poincaré Phys. Théor. 53 (1990), no. 4, 361–393 (English, with French summary). Hyperbolic behaviour of dynamical systems (Paris, 1990). MR 1096098
• Tosio Kato, Perturbation theory for linear operators, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1980 edition. MR 1335452
• G. Knieper, A second derivative formula of the Liouville entropy at spaces of constant negative curvature, Ergodic Theory Dynam. Systems 17 (1997), no. 5, 1131–1135. MR 1477035 (98h:58043)
• Hiroshi Kunita, Stochastic flows and stochastic differential equations, Cambridge Studies in Advanced Mathematics, vol. 24, Cambridge University Press, Cambridge, 1990. MR 1070361
• A. Lichnerowicz, Sur les espaces riemanniens complètement harmoniques, Bull. Soc. Math. France 72 (1944), 146–168. MR 0012886 (7,80c)
• F. Ledrappier, Ergodic properties of Brownian motion on covers of compact negatively-curve manifolds, Bol. Soc. Brasil. Mat. 19 (1988), no. 1, 115–140. MR 1018929 (91e:58210)
• F. Ledrappier, Harmonic measures and Bowen-Margulis measures, Israel J. Math. 71 (1990), no. 3, 275–287. MR 1088820
• François Ledrappier, Central limit theorem in negative curvature, Ann. Probab. 23 (1995), no. 3, 1219–1233. MR 1349169
• F. Ledrappier, Linear drift and entropy for regular covers, Geom. Func. Anal. 20 (2010), no. 3, 710–725. MR 2720229 (2011i:58060)
• François Ledrappier, Regularity of the entropy for random walks on hyperbolic groups, Ann. Probab. 41 (2013), no. 5, 3582–3605. MR 3127892
• François Ledrappier and Lin Shu, Entropy rigidity of symmetric spaces without focal points, Trans. Amer. Math. Soc. 366 (2014), no. 7, 3805–3820. MR 3192619
• François Ledrappier and Lin Shu, Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes, Ann. Inst. Fourier (Grenoble) 67 (2017), no. 3, 1115–1183 (English, with English and French summaries). MR 3668769
• X.-D. Li, Hamilton’s Harnack inequality and the W-entropy formula on complete Riemannian manifolds, Stochastic Process. Appl. 126 (2016), no. 4, 1264–1283. MR 3461198
• R. de la Llave, J. M. Marco, and R. Moriyón, Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation, Ann. of Math. (2) 123 (1986), no. 3, 537–611. MR 840722 (88h:58091)
• X. N. Ma and G. Marinescu, Exponential estimate for the asymptotics of Bergman kernels, Math. Ann. 362 (2015), no. 3-4, 1327–1347. MR 3368102
• Paul Malliavin, Stochastic calculus of variation and hypoelliptic operators, Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976) Wiley, New York-Chichester-Brisbane, 1978, pp. 195–263. MR 536013
• Paul Malliavin, Stochastic Jacobi fields, Partial differential equations and geometry (Proc. Conf., Park City, Utah, 1977) Lecture Notes in Pure and Appl. Math., vol. 48, Dekker, New York, 1979, pp. 203–235. MR 535595
• Paul Malliavin, $C^{k}$-hypoellipticity with degeneracy, Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1978) Academic Press, New York-London, 1978, pp. 199–214. MR 517243
• Paul Malliavin, $C^{k}$-hypoellipticity with degeneracy. II, Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1978) Academic Press, New York-London, 1978, pp. 327–340. MR 517250
• P. Malliavin, Stochastic analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 313, Springer-Verlag, Berlin, 1997. MR 1450093 (99b:60073)
• A. Manning, Topological entropy for geodesic flows, Ann. of Math. (2) 110 (1979), no. 3, 567–573. MR 0554385 (81e:58044)
• Anthony Manning, The volume entropy of a surface decreases along the Ricci flow, Ergodic Theory Dynam. Systems 24 (2004), no. 1, 171–176. MR 2041266
• P. Mathieu, Differentiating the entropy of random walks on hyperbolic groups, Ann. Probab. 43 (2015), no. 1, 166–187. MR 3298471
• M. Misiurewicz, On non-continuity of topological entropy, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 19 (1971), 319–320 (English, with Russian summary). MR 287578
• M. Misiurewicz, Diffeomorphism without any measure with maximal entropy, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 21 (1973), 903–910 (English, with Russian summary). MR 336764
• G. D. Mostow, Quasi-conformal mappings in $n$-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 53–104. MR 236383
• S. Newhouse, Continuity properties of entropy, Ann. of Math. (2) 129 (1989), no. 2, 215–235. and Corrections to: "Continuity properties of entropy” in Ann. of Math. (2) 131 (1990), no.2, 409–410. MR 0986792, MR 1043272
• A. A. Novikov, On moment inequalities and identities for stochastic integrals, Proceedings of the Second Japan-USSR Symposium on Probability Theory (Kyoto, 1972) Springer, Berlin, 1973, pp. 333–339. Lecture Notes in Math., Vol. 330. MR 0448553
• Mark A. Pinsky, Isotropic transport process on a Riemannian manifold, Trans. Amer. Math. Soc. 218 (1976), 353–360. MR 402957
• M. Pollicott, Analyticity of dimensions for hyperbolic surface diffeomorphisms, Proc. Amer. Math. Soc. 143 (2015), no. 8, 3465–3474. MR 3348789
• D. Revuz and M. Yor, Continuous martingales and Brownian motion, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293, Springer-Verlag, Berlin, 1999. Third edition. MR 1725357 (2000h:60050)
• S. Rosenberg, The Laplacian on a Riemannian manifold. An introduction to analysis on manifolds, London Mathematical Society Student Texts, 31, Cambridge University Press, Cambridge, 1997. MR 1462892 (98k:58206)
• D. Ruelle, Differentiation of SRB states, Comm. Math. Phys. 187 (1997), no. 1, 227–241. Correction and complements in Comm. Math. Phys. 234 (2003), 185–190. MR 1463827 (98k:58144), MR 1963142 (2004b:37038)
• David Ruelle, General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium, Phys. Lett. A 245 (1998), no. 3-4, 220–224. MR 1642617
• D. Ruelle, Differentiating the absolutely continuous invariant measure of an interval map $f$ with respect to $f$, Comm. Math. Phys. 258 (2005), no. 2, 445–453. MR 2171702 (2006i:37088)
• D. Ruelle, Differentiation of SRB states for hyperbolic flows, Ergodic Theory Dynam. Systems 28 (2008), no. 2, 613–631. MR 2408395 (2009k:37049)
• David Ruelle, A review of linear response theory for general differentiable dynamical systems, Nonlinearity 22 (2009), no. 4, 855–870. MR 2486360
• Hans Henrik Rugh, On the dimensions of conformal repellers. Randomness and parameter dependency, Ann. of Math. (2) 168 (2008), no. 3, 695–748. MR 2456882
• L. Saloff-Coste, Uniformly elliptic operators on Riemannian manifolds, J. Differential Geom. 36 (1992), no. 2, 417–450. MR 1180389 (93m:58122)
• Y. T. Siu, The complex analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. of Math. (2) 112 (1980), no. 1, 73–111. MR 0584075 (81j:53061)
• M. Shub, Global stability of dynamical systems. With the collaboration of Albert Fathi and Rémi Langevin, Translated from the French by Joseph Christy, Springer-Verlag, New York, 1987. MR 0869255 (87m:58086)
• A. V. Skorohod, A note on Gaussian measures in Banach space, Teor. Verojatnost. i Primenen 15 (1970), 519–520 (Russian, with English summary). MR 0277684
• Michael Spivak, A comprehensive introduction to differential geometry. Vol. II, 2nd ed., Publish or Perish, Inc., Wilmington, Del., 1979. MR 532831
• Daniel W. Stroock and James Turetsky, Upper bounds on derivatives of the logarithm of the heat kernel, Comm. Anal. Geom. 6 (1998), no. 4, 669–685. MR 1664888
• W. P. Thurston, The geometry and topology of three-manifolds, Electronic version 1.1, 2002.
• Shinzo Watanabe, Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels, Ann. Probab. 15 (1987), no. 1, 1–39. MR 877589
• Shing Tung Yau, On the heat kernel of a complete Riemannian manifold, J. Math. Pures Appl. (9) 57 (1978), no. 2, 191–201. MR 505904
• Y. Yomdin, Volume growth and entropy, Israel J. Math. 57 (1987), no. 3, 285–300. MR 889979
• Y. Yomdin, $C^k$-resolution of semialgebraic mappings. Addendum to: “Volume growth and entropy”, Israel J. Math. 57 (1987), no. 3, 301–317. MR 889980