Almost sure invariance principle for nonuniformly hyperbolic systems

Communications in Mathematical Physics

Volumn 260, Issue 1, 2005, Pages 131-146

  Melbourne, Ian ^a   Nicol, Matthew ^b  

^a UNIVERSITY OF SURREY   (United Kingdom)

^b University of Houston   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 25444432774     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1407-5     Document Type: Article

References (41)

1. Aaronson, J.: An Introduction to Infinite Ergodic Theory, Math. Surveys and Monographs 50, Providence, RI: Amer. Math. Soc., 1997
2. Aaronson, J., Denker, M.: Local limit theorems for partial sums of stationary sequences generated by Gibbs-Markov maps. Stoch. Dyn. 1, 193-237 (2001)
3. Alves, J., Luzzatto, S., Pinheiro, V.: Markov structures and decay of correlations for non-uniformly expanding dynamical systems. Ann. Inst. H. Poincaré, Anal. Non Linéaire, to appear
4. Baladi, V.: Positive Transfer Operators and Decay of Correlations. Advanced Series in Nonlinear Dynamics 16, Singapore: World Scientific, 2000
5. Baladi, V.: Decay of correlations. In: Katok, A. (ed.) et al., Smooth Ergodicity Theory and its Applications Proc. Symp. Pure Math. 69, Providence, RI: Amer. Math. Soc., 2001, pp. 297-325
6. Benedicks, M., Young, L.-S.: Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps. Ergod. Th. & Dynam. Sys. 12, 13-37 (1992)
7. Benedicks, M., Young, L.-S.: Sinai-Bowen-Ruelle measures for certain Hénon maps. Invent. Math. 112, 541-576 (1993)
8. Bowen, R.: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Math. 470, Berlin: Springer, 1975
9. Bruin, H., Holland, M., Nicol, M.: Livsic regularity for Markov systems. Ergod. Th. and Dyn. Syst. To appear
10. Bruin, H., Luzzatto, S., van Strien, S.: Decay of correlations in one-dimensional dynamics. Ann. Sci. École Norm. Sup. 36, 621-646 (2003)
11. Bunimovich, L.A., Sinaǐ, Y.G., Chemov, N.I.: Statistical properties of two-dimensional hyperbolic billiards. Uspekhi Mat. Nauk 46, 43-92 (1991)
12. Castro, A.: Backward inducing and exponential decay of correlations for partially hyperbolic attractors with mostly contracting direction. Ph. D. Thesis, IMPA (1998)
13. Chernov, N.: Statistical properties of piecewise smooth hyperbolic systems in high dimensions. Discrete Contin. Dynam. Systems 5, 425-448 (1999)
14. Chernov, N.: Decay of correlations and dispersing billiards. J. Stat. Phys. 94, 513-556 (1999)
15. Chernov, N., Young, L.S.: Decay of correlations for Lorentz gases and hard balls. In: Hard ball systems and the Lorentz gas. Encyclopaedia Math. Sci. 101, Berlin: Springer, 2000, pp. 89-120
16. Conze, J.-P., Le Borgne, S.: Méthode de martingales et flow géodésique sur une surface de courbure constante négative. Ergod. Th. & Dyn. Sys. 21, 421-441 (2001)
17. Denker. M., Philipp, W.: Approximation by Brownian motion for Gibbs measures and flows under a function. Ergod. Th. & Dyn. Sys. 4, 541-552 (1984)
18. Dolgopyat, D.: On dynamics of mostly contracting diffeomorphisms. Commun. Math. Phys. 213, 181-201 (2000)
19. Field, M.J., Melbourne, I., Török, A.: Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions. Ergod. Th. & Dyn. Sys. 23, 87-110 (2003)
20. Gordin, M.I.: The central limit theorem for stationary processes. Soviet Math. Dokl. 10, 1174-1176 (1969)
21. Gouëzel, S., Statistical properties of a skew product with a curve of neutral points. Preprint. 2004
22. Gouëzel, S.: Vitesse de décorrélation et théorèmes limites pour les applications non uniformément dilatantes. Ph. D. Thesis, Ecole Normale Supérieure, 2004
23. Hennion, H.: Sur un théorème spectral et son application aux noyaux lipchitziens. Proc. Amer. Math. Soc. 118, 627-634 (1993)
24. Hofbauer, F., Keller, G.: Ergodic properties of invariant measures for piecewise monotonic transformations. Math. Z. 180, 119-140 (1982)
25. Keller, G.: Un théorème de la limite centrale pour une classe de transformations monotones per morceaux. C. R. Acad. Sci. Paris 291, 155-158 (1980)
26. Liverani, C.: Central limit theorem for deterministic systems. In: International Conference on Dynamical Systems (F. Ledrappier, J. Lewowicz and S. Newhouse, eds.), Pitman Research Notes in Math. 362, Harlow: Longman Group Ltd, 1996, pp. 56-75
27. Liverani, C., Saussol, B., Vaienti, S.: A probabilistic approach to intermittency. Ergod Th. and Dyn. Sys. 19, 671-685 (1999)
28. Melbourne, I., Nicol, M.: Statistical properties of endomorphisms and compact group extensions. J. London Math. Soc. 70, 427-446 (2004)
29. Melbourne, I., Török, A.: Central limit theorems and invariance principles for time-one maps of hyperbolic flows. Commun. Math. Phys. 229, 57-71 (2002)
30. Melbourne, I.,Török, A.: Statistical limit theorems for suspension flows. Israeli. Math. 194, 191-210 (2004)
31. Parry, W., Pollicott, M.: Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics. Astérique 187-188, Montrouge: Société Mathématique de France, 1990
32. Philipp, W., Stout, W.F.: Almost Sure Invariance Principles for Partial Sums of Weakly Dependent Random Variables. Mem. of the Amer. Math. Soc. 161, Providence, RI: Amer. Math. Soc., 1975
33. Pollicott, M., Sharp, R.: Invariance principles for interval maps with an indifferent fixed point. Commun. Math. Phys. 229, 337-346 (2002)
34. Ratner, M.: The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature. Israel J. Math. 16, 181-197 (1973)
35. Ruelle, D.: Thermodynamic Formalism. Encyclopedia of Math. and its Applications 5, Reading, Massachusetts: Addison Wesley, 1978
36. Sinaǐ, Y.G.: Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards. Uspehi Mat. Nauk 25, 141-192 (1970)
37. Sinaǐ, Y.G.: Gibbs measures in ergodic theory. Russ. Math. Surv. 27, 21-70 (1972)
38. Viana, M.: Stochastic dynamics of deterministic systems. Col. Bras, de Matemática, 1997
39. Walkden, C.P.: Invariance principles for iterated maps that contract on average. Preprint, 2003
40. Young, L.-S.: Statistical properties of dynamical systems with some hyperbolicity. Ann. of Math. 147, 585-650 (1998)
41. Young, L.-S.: Recurrence times and rates of mixing. Israel J. Math. 110, 153-188 (1999)