On dynamics of mostly contracting diffeomorphisms

Communications in Mathematical Physics

Volumn 213, Issue 1, 2000, Pages 181-201

  Dolgopyat, Dmitry ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034349951     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200000238     Document Type: Article

References (40)

1. 1. Alves, J.: SRB measures for nonhyperbolic systems with multidimensional expansion. IMPA Thesis, 1997
2. 2. Alves, J., Bonatti, C. & Viana M.: SRB measures for partially hyperbolic diffeomorphisms: The expanding case. Preprint
3. 3. Benedics, M. & Young, L.-S.: Sinai-Bowen-Ruelle measures for certain Henon maps. Inv. Math. 112, 541-576 (1993)
4. 4. Bonatti, C. & Viana, M.: SRB measures for partially hyperbolic systems those central direction is mostly contracting. To appear in Israel Math. J.
5. 5. Bougerol, P. & Lacroix, J.: Products of random matrices with applications to Schrödinger operators. Boston-Basel-Stuttgart: Birkhäuser, 1985
6. 6. Brin, M. & Pesin, Ya. B.: Partially hyperbolic dynamical systems. Math. USSR-Izvestiya 8, 177-218 (1974)
7. 7. Burns, K., Pugh, C. & Wilkinson, A.: Stable ergodicity and Anosov flows. Preprint
8. 8. Burns, K. & Wilkinson, A.: Stable ergodicity of skew products Preprint
9. 9. Castro, A.: Backwards inducing and decay of correlations for certain partially hyperbolic maps whose central direction is mostly contracting. IMPA Thesis, 1998
10. 10. Chernov, N. I.: Decay of correlations and dispersing billiards. J. Stat. Phys. 94, 513-556 (1999)
11. 11. Chernov, N. I. & Haskell, C.: Nonuniformly hyperbolic K-systems are Bernoulli: Erg. Th. & Dyn. Sys. 16, 19-44 (1996)
12. 12. Dolgopyat, D.: Limit theorems for partially hyperbolic systems. Preprint
13. 13. Grayson, M., Pugh C. & Shub M. Stably ergodic diffeomorphisms. Ann. Math. 140, 295-329 (1994)
14. 14. Hirsh, M., Pugh C. & Shub, M.: Invariant manifolds. Lect. Notes in Math. 583. Berlin: Springer-Verlag, 1977
15. 15. Katok, A. & Hasselblatt B.: Introduction to the modern theory of dynamical systems. Encyclopedia Math., Appl. 54, Cambridge: Cambridge University Press, 1998
16. 16. Katok, A.& Kononenko, A.: Cocycle stability for partially hyperbolic systems. Math. Res. Lett. 3, 191-210 (1996)
17. 17. Margulis, G. A.: Certain measures that are connected with U-flows on compact manifolds. Func. Anal. Appl. 4, 62-76 (1970)
18. 18. Margulis, G. A.: PhD Thesis, Moscow State University, 1970
19. 19. Milnor, J.: On the concept of attractor. Commun. Math. Phys. 99, 177-195 (1985) and 102, 517-519 (1985)
20. 19. Milnor, J.: On the concept of attractor. Commun. Math. Phys. 99, 177-195 (1985) and 102, 517-519 (1985)
21. 20. Nitica, V. & Torok, A.: An open dense set of stably ergodic diffeomorphisms in a neighbourhood of a non-ergodic one. To appear in Topology
22. 21. Ornstein, D. & Weiss, B.: On Bernoulli nature of systems with some hyperbolic structure. Erg. Th. & Dyn. Sys. 18, 441-456 (1998)
23. 22. Palis, J.: Global view on dynamics. To appear in Asterisque
24. 23. Palis, J., Pugh, C. C. & Robinson, R. C.: Nondifferentiability of invariant foliations. Lecture Notes Math. 468, Berlin: Springer, 1975, pp. 234-240
25. 24. Pesin, Ya. B.: Families of invariant manifolds that correspond to nonzero characteristic exponents. Izv. Akad. Nauk SSSR 40, 1332-1379 (1976)
26. 25. Pesin, Ya. B.: Characteristic Lyapunov exponents, and smooth ergodic theory. Uspehi Mat. Nauk 32, 55-112 (1977)
27. 26. Pesin, Ya. B. & Sinai, Ya. G.: Gibbs measures for partially hyperbolic attractors. Erg. Th. & Dyn. Sys. 2, 417-438 (1982)
28. 27. Pugh, C. & Shub, M.: Ergodic attractors. Trans. AMS 312, 1-54 (1989)
29. 28. Pugh, C. & Shub, M.: Stably ergodic dynamical systems and partial hyperbolicity. J. Complexity 13, 125-179 (1997)
30. 29. Pugh, C. & Shub, M.: Stable ergodicity and Julienne quasi-conformality. Preprint
31. 30. Ruelle, D.: A measure associated with Axiom A attractors. Am. J. Math. 98, 619-654 (1976)
32. 31. Ruelle, D.: Differentiation of SRB states. Commun. Math. Phys. 187, 227-241 (1997)
33. 32. Shub, M. & Wilkinson A.: Pathological foliations and removable zero exponents. Inv. Math. (1999)
34. 33. Sinai, Ya. G.: Classical dynamic systems with countably-multiple Lebesgue spectrum. II. Izv. Akad. Nauk SSSR Ser. Mat. 30, 15-68 (1966)
35. 34. Sinai, Ya. G.: Gibbs measures in ergodic theory. Uspehi Mat. Nauk 27, 21-64 (1972)
36. 35. Sinai, Ya. G.: Stochasticity of dynamical systems. In: Nonlinear waves, Edited by A. V. Gaponov-Grekhov Moscow: Nauka, 1979, pp. 192-211
37. 36. Viana, M.: Multidimensional nonhyperbolic attractors. Publ. IHES 85, 63-96 (1997)
38. 37. Wilkinson, A.: Stable ergodicity of time-one map of a geodesic flow: PhD Thesis, University of California at Berkeley, 1995
39. 38. Young, L.-S.: Statistical properties of dynamical systems with some hyperbolicity including certain billiards. Ann. Math. 147, 585-650 (1998)
40. 39. Young, L.-S.: Recurrence times and rates of mixing. Isr. J. Math 110, 153-188 (1999)