On the geometry and dynamics of diffeomorphisms of surfaces

Thurston, William P.

doi:10.1090/S0273-0979-1988-15685-6

On the geometry and dynamics of diffeomorphisms of surfaces
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Bull. Amer. Math. Soc. 19 (1988), 417-431

References

D. V. Anosov, Geodesic flows on closed Riemannian manifolds of negative curvature, Trudy Mat. Inst. Steklov. 90 (1967), 209 (Russian). MR 0224110
Pierre Arnoux and Jean-Christophe Yoccoz, Construction de difféomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 1, 75–78 (French, with English summary). MR 610152
Lipman Bers, An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978), no. 1-2, 73–98. MR 477161, DOI 10.1007/BF02545743
Lipman Bers, On boundaries of Teichmüller spaces and on Kleinian groups. I, Ann. of Math. (2) 91 (1970), 570–600. MR 297992, DOI 10.2307/1970638
Lipman Bers, On iterates of hyperbolic transformations of Teichmüller space, Amer. J. Math. 105 (1983), no. 1, 1–11. MR 692104, DOI 10.2307/2374379
Joan S. Birman and Mark E. Kidwell, Fixed points of pseudo-Anosov diffeomorphisms of surfaces, Adv. in Math. 46 (1982), no. 2, 217–220. MR 679909, DOI 10.1016/0001-8708(82)90024-X
Francis Bonahon, Cobordism of automorphisms of surfaces, Ann. Sci. École Norm. Sup. (4) 16 (1983), no. 2, 237–270. MR 732345, DOI 10.24033/asens.1448
Francis Bonahon, Bouts des variétés hyperboliques de dimension $3$, Ann. of Math. (2) 124 (1986), no. 1, 71–158 (French). MR 847953, DOI 10.2307/1971388
Andrew J. Casson and Steven A. Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Mathematical Society Student Texts, vol. 9, Cambridge University Press, Cambridge, 1988. MR 964685, DOI 10.1017/CBO9780511623912
A. J. Casson and D. D. Long, Algorithmic compression of surface automorphisms, Invent. Math. 81 (1985), no. 2, 295–303. MR 799268, DOI 10.1007/BF01389054
Marc Culler and John W. Morgan, Group actions on $\textbf {R}$-trees, Proc. London Math. Soc. (3) 55 (1987), no. 3, 571–604. MR 907233, DOI 10.1112/plms/s3-55.3.571
Marc Culler and Peter B. Shalen, Varieties of group representations and splittings of $3$-manifolds, Ann. of Math. (2) 117 (1983), no. 1, 109–146. MR 683804, DOI 10.2307/2006973
M. Culler and P. B. Shalen, Bounded, separating, incompressible surfaces in knot manifolds, Invent. Math. 75 (1984), no. 3, 537–545. MR 735339, DOI 10.1007/BF01388642
Albert Fathi and François Laudenbach, Difféomorphismes pseudo-Anosov et décomposition de Heegaard, C. R. Acad. Sci. Paris Sér. A-B 291 (1980), no. 6, A423–A425 (French, with English summary). MR 596088
Albert Fathi, Dehn twists and pseudo-Anosov diffeomorphisms, Invent. Math. 87 (1987), no. 1, 129–151. MR 862715, DOI 10.1007/BF01389156
Travaux de Thurston sur les surfaces, Astérisque, vol. 66, Société Mathématique de France, Paris, 1979 (French). Séminaire Orsay; With an English summary. MR 568308
David Fried, Transitive Anosov flows and pseudo-Anosov maps, Topology 22 (1983), no. 3, 299–303. MR 710103, DOI 10.1016/0040-9383(83)90015-0
David Fried, Flow equivalence, hyperbolic systems and a new zeta function for flows, Comment. Math. Helv. 57 (1982), no. 2, 237–259. MR 684116, DOI 10.1007/BF02565860
David Fried, Growth rate of surface homeomorphisms and flow equivalence, Ergodic Theory Dynam. Systems 5 (1985), no. 4, 539–563. MR 829857, DOI 10.1017/S0143385700003151
Marlies Gerber and Anatole Katok, Smooth models of Thurston’s pseudo-Anosov maps, Ann. Sci. École Norm. Sup. (4) 15 (1982), no. 1, 173–204. MR 672479, DOI 10.24033/asens.1424
Jane Gilman, On the Nielsen type and the classification for the mapping class group, Adv. in Math. 40 (1981), no. 1, 68–96. MR 616161, DOI 10.1016/0001-8708(81)90033-5
Jane Gilman, Determining Thurston classes using Nielsen types, Trans. Amer. Math. Soc. 272 (1982), no. 2, 669–675. MR 662059, DOI 10.1090/S0002-9947-1982-0662059-X
Frederick P. Gardiner, Teichmüller theory and quadratic differentials, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1987. A Wiley-Interscience Publication. MR 903027
Michael Handel, Global shadowing of pseudo-Anosov homeomorphisms, Ergodic Theory Dynam. Systems 5 (1985), no. 3, 373–377. MR 805836, DOI 10.1017/S0143385700003011
Michael Handel, Entropy and semi-conjugacy in dimension two, Ergodic Theory Dynam. Systems 8 (1988), no. 4, 585–596. MR 980798, DOI 10.1017/S0143385700004703
Michael Handel and William P. Thurston, Anosov flows on new three manifolds, Invent. Math. 59 (1980), no. 2, 95–103. MR 577356, DOI 10.1007/BF01390039
Michael Handel and William P. Thurston, New proofs of some results of Nielsen, Adv. in Math. 56 (1985), no. 2, 173–191. MR 788938, DOI 10.1016/0001-8708(85)90028-3
A. Hatcher and W. Thurston, Incompressible surfaces in $2$-bridge knot complements, Invent. Math. 79 (1985), no. 2, 225–246. MR 778125, DOI 10.1007/BF01388971
John L. Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. (2) 121 (1985), no. 2, 215–249. MR 786348, DOI 10.2307/1971172
John Hubbard and Howard Masur, Quadratic differentials and foliations, Acta Math. 142 (1979), no. 3-4, 221–274. MR 523212, DOI 10.1007/BF02395062
Steven P. Kerckhoff, The asymptotic geometry of Teichmüller space, Topology 19 (1980), no. 1, 23–41. MR 559474, DOI 10.1016/0040-9383(80)90029-4
Steven P. Kerckhoff, The Nielsen realization problem, Ann. of Math. (2) 117 (1983), no. 2, 235–265. MR 690845, DOI 10.2307/2007076
Steven P. Kerckhoff, Earthquakes are analytic, Comment. Math. Helv. 60 (1985), no. 1, 17–30. MR 787659, DOI 10.1007/BF02567397
Steven Kerckhoff, Howard Masur, and John Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. of Math. (2) 124 (1986), no. 2, 293–311. MR 855297, DOI 10.2307/1971280
Irwin Kra, On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981), no. 3-4, 231–270. MR 611385, DOI 10.1007/BF02392465
Howard Masur, Interval exchange transformations and measured foliations, Ann. of Math. (2) 115 (1982), no. 1, 169–200. MR 644018, DOI 10.2307/1971341
Howard Masur, Ergodic actions of the mapping class group, Proc. Amer. Math. Soc. 94 (1985), no. 3, 455–459. MR 787893, DOI 10.1090/S0002-9939-1985-0787893-5
Howard Masur, Two boundaries of Teichmüller space, Duke Math. J. 49 (1982), no. 1, 183–190. MR 650376
Richard T. Miller, Geodesic laminations from Nielsen’s viewpoint, Adv. in Math. 45 (1982), no. 2, 189–212. MR 664623, DOI 10.1016/S0001-8708(82)80003-0
John W. Morgan and Peter B. Shalen, Valuations, trees, and degenerations of hyperbolic structures. I, Ann. of Math. (2) 120 (1984), no. 3, 401–476. MR 769158, DOI 10.2307/1971082
John W. Morgan and Peter B. Shalen, Degenerations of hyperbolic structures. II. Measured laminations in $3$-manifolds, Ann. of Math. (2) 127 (1988), no. 2, 403–456. MR 932305, DOI 10.2307/2007061
John W. Morgan and Peter B. Shalen, Degenerations of hyperbolic structures. II. Measured laminations in $3$-manifolds, Ann. of Math. (2) 127 (1988), no. 2, 403–456. MR 932305, DOI 10.2307/2007061
Lee Mosher, The classification of pseudo-Anosovs, Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984) London Math. Soc. Lecture Note Ser., vol. 112, Cambridge Univ. Press, Cambridge, 1986, pp. 13–75. MR 903858
Jakob Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, Acta Math. 50 (1927), no. 1, 189–358 (German). MR 1555256, DOI 10.1007/BF02421324
Jakob Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. II, Acta Math. 53 (1929), no. 1, 1–76 (German). MR 1555290, DOI 10.1007/BF02547566
Jakob Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. III, Acta Math. 58 (1932), no. 1, 87–167 (German). MR 1555345, DOI 10.1007/BF02547775
Ulrich Oertel, Measured laminations in $3$-manifolds, Trans. Amer. Math. Soc. 305 (1988), no. 2, 531–573. MR 924769, DOI 10.1090/S0002-9947-1988-0924769-1
Athanase Papadopoulos, Difféomorphismes pseudo-Anosov et automorphismes symplectiques de l’homologie, Ann. Sci. École Norm. Sup. (4) 15 (1982), no. 3, 543–546 (French). MR 690652, DOI 10.24033/asens.1436
Athanase Papadopoulos, L’extension du flot de Fenchel-Nielsen au bord de Thurston de l’espace de Teichmüller, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 8, 325–327 (French, with English summary). MR 838585
Athanase Papadopoulos, Geometric intersection functions and Hamiltonian flows on the space of measured foliations on a surface, Pacific J. Math. 124 (1986), no. 2, 375–402. MR 856170, DOI 10.2140/pjm.1986.124.375
Athanase Papadopoulos, Sur le bord de Thurston de l’espace de Teichmüller d’une surface non compacte, Math. Ann. 282 (1988), no. 3, 353–359 (French). MR 967017, DOI 10.1007/BF01460038
Athanase Papadopoulos, Sur le bord de Thurston de l’espace de Teichmüller d’une surface non compacte, Math. Ann. 282 (1988), no. 3, 353–359 (French). MR 967017, DOI 10.1007/BF01460038
Mary Rees, An alternative approach to the ergodic theory of measured foliations on surfaces, Ergodic Theory Dynam. Systems 1 (1981), no. 4, 461–488 (1982). MR 662738, DOI 10.1017/s0143385700001383
Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504, DOI 10.1007/978-3-642-61856-7
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1
Kurt Strebel, Quadratic differentials, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 5, Springer-Verlag, Berlin, 1984. MR 743423, DOI 10.1007/978-3-662-02414-0
Dennis Sullivan, Travaux de Thurston sur les groupes quasi-fuchsiens et les variétés hyperboliques de dimension $3$ fibrées sur $S^{1}$, Bourbaki Seminar, Vol. 1979/80, Lecture Notes in Math., vol. 842, Springer, Berlin-New York, 1981, pp. 196–214 (French). MR 636524
William A. Veech, Projective Swiss cheeses and uniquely ergodic interval exchange transformations, Ergodic theory and dynamical systems, I (College Park, Md., 1979–80), Progr. Math., vol. 10, Birkhäuser, Boston, Mass., 1981, pp. 113–193. MR 633764
William A. Veech, The Teichmüller geodesic flow, Ann. of Math. (2) 124 (1986), no. 3, 441–530. MR 866707, DOI 10.2307/2007091
Friedhelm Waldhausen, On irreducible $3$-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56–88. MR 224099, DOI 10.2307/1970594
Heiner Zieschang, Finite groups of mapping classes of surfaces, Lecture Notes in Mathematics, vol. 875, Springer-Verlag, Berlin, 1981. MR 643627, DOI 10.1007/BFb0090465
Jakob Nielsen, Surface transformation classes of algebraically finite type, Danske Vid. Selsk. Mat.-Fys. Medd. 21 (1944), no. 2, 89. MR 15791