Limit theorems and Markov approximations for chaotic dynamical systems

Probability Theory and Related Fields

Volumn 101, Issue 3, 1995, Pages 321-362

  Chernov, N I ^a  

^a UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

Author keywords

Mathematics Subject Classification: 28D05, 58F11, 58F15, 60F05, 60F17

Indexed keywords

EID: 21844520203     PISSN: 01788051     EISSN: 14322064     Source Type: Journal    
DOI: 10.1007/BF01200500     Document Type: Article

References (50)

1. Entropy a complete metric invariant for automorphisms of the torus
2. On the central limit question under absolute regularity
3. Statistical properties of Lorentz gas with periodic configuration of scatterers
4. Markov partitions for dispersed billiards
5. Markov partitions for two-dimensional billiards
6. Statistical properties of two-dimensional hyperbolic billiards
7. On the central limit theorem for dynamical systems
8. Statistical properties of the periodic Lorentz gas. Multidimensional case
9. Decay of correlations in a chaotic measure-preserving transformation
10. The central limit theorem for dynamical systems
11. Central limit theorem for nonstationary Markov chains I
12. Billiards and Bernoulli schemes
13. Sporadicity: between periodic and chaotic dynamical behaviors
14. Ergodic properties of invariant measures for piecewise monotonic transformations
15. Some limit theorems for stationary processes
16. A central limit theorem of mixed type for a class of 1-dimensional transformations
17. Perron Frobenius operator and central limit theorem
18. Counterexamples in ergodic theory and number theory
19. Un théorème de la limite centrale pour une classe de transformations monotonnes par morceaux
20. Spectral theory, zeta functions and the distributions of periodic points for Collet-Eckmann maps
21. Markov partitions and shadowing for nonuniformly hyperbolic systems with singularities
22. Statistical properties of a nonuniformly hyperbolic map of the interval
23. On the dispersion of time-dependent means of a stationary stochastic process
24. On the intermittency of a piecewise linear map
25. Finite coarse-graining and Chapman-Kolmogorov equation in conservative dynamical systems
26. Functional central limit theorems for strictly stationary processes satisfying the strong mixing condition
27. Recent advances in the central limit theorem and its weak invariance principle for mixing sequences of random variables (A survey)
28. Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties
29. Invariance principles for independent and weakly dependent random variables
30. Maps of intervals with indifferent fixed points: thermodynamic formalism and phase transition
31. The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature
32. A measure associated with Axiom-A attractors
33. Bounded variation and invariant measures
34. Invariant measures for hyperbolic maps with singularities
35. Markov partitions and C-diffeomorphisms
36. Dynamical systems with elastic reflections. Ergodic properties of scattering billiards
37. Gibbs measures in ergodic theory
38. Differentiable dynamical systems
39. On limit theorems and category for dynamical systems
40. Statistical physics of temporal intermittency
41. Decay of correlations for certain quadratic maps
42. Almost sure invariance principle for some maps of an interval