Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Tangent bundles to regular basic sets in hyperbolic dynamics

Author: Luchezar Stoyanov
Journal: Proc. Amer. Math. Soc. 140 (2012), 1623-1631
MSC (2010): Primary 37D20, 37D40
Posted: August 18, 2011
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Given a locally maximal compact invariant hyperbolic set $\Lambda$ for a flow or diffeomorphism on a Riemann manifold with stable laminations, we construct an invariant continuous bundle of tangent vectors to local unstable manifolds that locally approximates $\Lambda$ in a certain way.

References

Bibliography

[B] Rufus Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429–460. MR 0339281 (49 #4041)
[Ch] N. Chernov, Invariant measures for hyperbolic dynamical systems, Handbook of dynamical systems, Vol. 1A, North-Holland, Amsterdam, 2002, pp. 321–407. MR 1928521 (2003g:37047), http://dx.doi.org/10.1016/S1874-575X(02)80006-6
[D] Dmitry Dolgopyat, On decay of correlations in Anosov flows, Ann. of Math. (2) 147 (1998), no. 2, 357–390. MR 1626749 (99g:58073), http://dx.doi.org/10.2307/121012
[GP] Victor Guillemin and Alan Pollack, Differential topology, Prentice-Hall Inc., Englewood Cliffs, N.J., 1974. MR 0348781 (50 #1276)
[Ha] Boris Hasselblatt, Regularity of the Anosov splitting and of horospheric foliations, Ergodic Theory Dynam. Systems 14 (1994), no. 4, 645–666. MR 1304137 (95j:58130), http://dx.doi.org/10.1017/S0143385700008105
[Ka] Michael Kapovich, Kleinian groups in higher dimensions, Geometry and dynamics of groups and spaces, Progr. Math., vol. 265, Birkhäuser, Basel, 2008, pp. 487–564. MR 2402415 (2009g:30043), http://dx.doi.org/10.1007/978-3-7643-8608-5_13
[KH] Anatole Katok and Boris Hasselblatt, Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its Applications, vol. 54, Cambridge University Press, Cambridge, 1995. With a supplementary chapter by Katok and Leonardo Mendoza. MR 1326374 (96c:58055)
[M] B. Malgrange, Ideals of differentiable functions, Tata Institute of Fundamental Research Studies in Mathematics, No. 3, Tata Institute of Fundamental Research, Bombay, 1967. MR 0212575 (35 #3446)
[PSW] Charles Pugh, Michael Shub, and Amie Wilkinson, Hölder foliations, Duke Math. J. 86 (1997), no. 3, 517–546. MR 1432307 (97m:58155), http://dx.doi.org/10.1215/S0012-7094-97-08616-6
Charles Pugh, Michael Shub, and Amie Wilkinson, Correction to: “Hölder foliations” [Duke Math. J. 86 (1997), no. 3, 517–546; MR1432307 (97m:58155)], Duke Math. J. 105 (2000), no. 1, 105–106. MR 1788044 (2001h:37057), http://dx.doi.org/10.1215/S0012-7094-00-10515-7
[Ratc] John G. Ratcliffe, Foundations of hyperbolic manifolds, Graduate Texts in Mathematics, vol. 149, Springer-Verlag, New York, 1994. MR 1299730 (95j:57011)
[St1] Latchezar Stoyanov, Exponential instability for a class of dispersing billiards, Ergodic Theory Dynam. Systems 19 (1999), no. 1, 201–226. MR 1677157 (99m:58149), http://dx.doi.org/10.1017/S0143385799126543
[St2] L. Stoyanov, Spectra of Ruelle transfer operators for Axiom A flows, Nonlinearity 24 (2011), 1089-1120.
[St3] L. Stoyanov, Non-integrability of open billiard flows and Dolgopyat type estimates, Ergod. Th. & Dynam. Sys., to appear, http://dx.doi.org/10.1017/S0143385710000933.
[St4] L. Stoyanov, Pinching conditions, linearization and regularity of Axiom A flows, preprint (arXiv: math.DS:1010.1594).
[Su] Dennis Sullivan, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984), no. 3-4, 259–277. MR 766265 (86c:58093), http://dx.doi.org/10.1007/BF02392379

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|