Livšic regularity for Markov systems

Ergodic Theory and Dynamical Systems

Volumn 25, Issue 6, 2005, Pages 1739-1765

  Bruin, Henk ^a   Holland, Mark ^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: 26044447595     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385705000179     Document Type: Article

References (42)

1. J. Aaronson and M. Denker. Local limit theorems for partial sums of stationary sequences generated by Gibbs-Markov maps. Stochast. Dynam. 1 (2001), 193-237.
2. J. Aaronson, M. Denker, O. Sarig and R. Zweimüller. Aperiodicity of cocycles and stochastic properties of non-Markov maps. Stochast. Dynam. 4 (2004), 31-62.
3. J. Alves, S. Luzzatto and V. Pinheiro. Markov structures and decay of correlations for non-uniformly expanding dynamical systems. Ann. Inst. Henri Poincaré to appear.
4. V. Baladi. Positive Transfer Operators and Decay of Correlations (Adv. Series Nonlin. Dynam., 16). World Scientific, Singapore, 2000.
5. M. Benedicks and L. Carleson. The dynamics of the Hénon map. Ann. Math. 133 (1991), 73-69.
6. L. Breiman. Probability (Classics Appl. Math., 7). SIAM, Philadelphia, PA, 1992.
7. T. Bröcker and T. Dieck. Representations of Compact Lie Groups. Springer, New York, 1985.
8. H. Bruin and S. Luzzatto. Topological invariance of the sign of the Lyapunov exponents in one-dimensional maps. Proc. Amer. Math. Soc. to appear.
9. H. Bruin, S. Luzzatto, and S. van Strien. Decay of correlations in one-dimensional dynamics. Ann. Sci. École Norm. Sup. 36 (2003), 621-646.
10. H. Bruin and S. van Strien. Existence of acips for multimodal maps. Global Analysis of Dynamical Systems, Festschrift dedicated to Floris Takens for his 60th birthday (2001).
11. H. Bruin and S. Vaienti. Return time statistics for unimodal maps. Fund. Math. 176 (2003), 77-94.
12. M. Benedicks and L. S. Young. Markov extensions and decay of correlations of certain Hénon maps. Astérisque 261 (2000), 13-56.
13. R. de la Llave, J. M. Marco and E. Moriyon. Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomological equation. Ann. Math. 123 (1986), 537-611.
14. S. Gouëzel. Sharp polynomial estimates for the decay of correlations. Israel J. Math. 139 (2004), 29-65.
15. S. Gouëzel. Decay of correlations for non-uniformly expanding dynamical systems. Bull. Soc. Math. France to appear.
16. S. Gouëzel. Regularity of coboundaries for non uniformly expanding Markov maps. Proc. Amer. Math. Soc, to appear.
17. F. Hofbauer. On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. Israel J. Math. 34 (1979), 213-237.
18. O. Jenkinson. Smooth cocycle rigidity for expanding maps and an application to Mostow rigidity. Math. Proc. Comb. Phil. Soc. 132 (2002), 439-452.
19. A. Katok and B. Hasselblatt. Introduction to the modern theory of dynamical systems (Encyclopedia Math. Appl., 54). Cambridge University Press, Cambridge, 1995.
20. G. Keller. Equilibrium States in Ergodic Theory. Cambridge University Press, Cambridge, 1988.
21. G. Keller. Exponents, attractors and Hopf decompositions for interval maps. Ergod. Th. & Dynam. Sys. 10 (1990), 717-744.
22. G. Keller. Lifting measures to Markov extensions. Monatsh. Math. 108 (1989), 183-200.
23. H. Keynes and D. Newton. Ergodic measures for non-abelian compact group extensions. Compositio Math. 32 (1976), 53-70.
24. A. N. Livšic. Cohomology of dynamical systems. Math. USSR Izv. 6 (1972), 1278-1301.
25. A. N. Livšic. Homology properties of Y-systems. Math. Notes 10 (1971), 758-763.
26. R. Mañé, Ergodic Theory and Differentiable Dynamics. Springer, Berlin, 1987.
27. W. de Melo and S. van Strien. One-dimensional Dynamics. Springer, Berlin, 1993.
28. M. Nicol and M. Pollicott. Measurable cocycle rigidity for some noncompact groups. Bull. Lond. Math. Soc. 31 (1999), 592-600.
29. M. Nicol and M. Pollicott. Livšic theorems for semisimple Lie groups. Ergod. Th. & Dynam. Sys. 21 (2001), 1501-1509.
30. M. Nicol and A. Scott. Livšic theorem and stable ergodicity for group extensions of hyperbolic systems with discontinuities. Ergod. Th. & Dynam. Sys. 23 (2003), 1867-1889.
31. M. Noorani. Ergodicity and weak-mixing of homogeneous extensions of measure-preserving transformations with applications to Markov shifts. Monatsh. Math. 123 (1997), 149-170.
32. T. Nowicki and S. van Strien. Invariant measures exist under a summability condition. Invent. Math. 105 (1991), 123-136.
33. W. Parry and M. Pollicott. The Livsic cocycle equation for compact Lie group extensions of hyperbolic systems. J. London Math. Soc. (2) 56 (1997), 405-416.
34. M. Pollicott and C. Walkden. Livšic theorems for connected Lie groups. Trans. Amer. Math. Soc. 353 (2001), 2879-2895.
35. M. Pollicott and M. Yuri. Regularity of solutions to the measurable Livsic equation. Trans. Amer. Math. Soc. 351 (1999), 559-568.
36. A. Scott. Livšic theorems for unimodal maps. Preprint, 2004.
37. A. Scott. Livšic theorems and the stable ergodicity of compact group extensions of systems with some hyperbolicity. PhD Thesis, University of Surrey, 2003.
38. C. Walkden. Livsic theorems for hyperbolic flows. Trans. Amer. Math. Soc. 352 (2000), 1299-1313.
39. C. Walkden. Livsic regularity theorems for twisted cocycle equations over hyperbolic systems. J. London Math. Soc. 61 (2000), 286-300.
40. Q. Wang and L.-S. Young. Strange attractors with one direction of instability. Comm. Math. Phys. 218 (2001), 1-97.
41. L.-S. Young. Recurrence times and rates of mixing. Israel J. Math. 110 (1999), 153-188.
42. L.-S. Young. Statistical properties of dynamical systems with some hyperbolicity. Ann. Math. 147 (1998), 585-650.