Correlation decay for Markov maps on a countable state space

Ergodic Theory and Dynamical Systems

Volumn 21, Issue 1, 2001, Pages 165-196

  Maume Deschamps, Véronique ^a  

^a UNIVERSITÉ DE BOURGOGNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035631263     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385701001110     Document Type: Article

References (30)

1. J. Aaronson, M. Denker and M. Urbanski. Ergodic theory for Markov fibered systems and parabolic rational maps. Trans. Amer. Math. Soc. 337(2) (1993), 495-548.
2. V. Baladi, A. Kondah and B. Schmitt. Random correlations for small perturbations of expanding maps. Random & Comput. Dyn. 4 (1996), 179-204.
3. M. Benedicks and L.-S. Young. Markov extensions and decay of correlations for certain Henon maps. Asterisque No. 261 (2000), 13-56.
4. G. Birkhoff. Extensions of Jentzch's theorem. Trans. Amer. Math. Soc. 85 (1957), 219-227.
5. G. Birkhoff. Lattice Theory, 3rd edition. American Mathematical Society, 1967.
6. T. Bogenschütz. Equilibrium states for random dynamical systems. Ph.D. Thesis, University of Bremen, 1991.
7. X. Bressaud. Subshifts on an infinite alphabet. Ergod. Th. & Dynam. Sys. 19(5) (1999), 1175-1200.
8. J. Buzzi. Exponential decay of correlations for random Lasota-Yorke maps. Commun. Math. Phys. 208(1) (1999), 25-54.
9. P. Ferrero and B. Schmitt. Ruelle Perron Frobenius theorems and projective metrics. Colloque Math. Soc. J. Bolyai Random Fields, Estergom, Hungary, 1979.
10. P. Ferrero and B. Schmitt. On the rate of convergence for some limit ratio theorems related to endomorphisms with a non-regular invariant density. Preprint, 1994.
11. A. Galves and B. Schmitt. Inequalities for hitting time in mixing dynamical systems. Random & Comput. Dyn. 5 (1997), 337-348.
12. P. Gaspard and X. J. Wang. Proc. Math. Acad. Sci. USA 85 (1988), 4591.
13. H. Hu. Decay of correlations for maps with indifferent fixed points. Preprint, 1998.
14. C. T. Ionescu and G. Marinescu. Théorie ergodique pour des classes d'opérations non-complètement continues. Ann. Math. 52 (1950), 140-147.
15. A. Kondah, V. Maume and B. Schmitt. Vitesse de convergence vers l'état d'équlibre pour des dynamiques markoviennes non höldériennes. Ann. Inst. Poincaré Sec. Prob. Stat. 33(6) (1997), 675-695.
16. A. Lambert, S. Siboni and S. Vaienti. Statistical properties of a non-uniformly hyperbolic map of the interval. J. Stat. Phys. 72 (1993), 1305-1330.
17. C. Liverani. Decay of correlations in piecewise expanding maps. J. Stat. Phys. 78(3/4) (1995), 1111-1129.
18. C. Liverani. Decay of correlations. Ann. Math. 142(2) (1995), 239-301.
19. C. Liverani. Central limit theorem for deterministic systems. Proc. Int. Congress on Dynamical Systems (Montevideo 95) (Research Notes in Mathematics Series). Pittman, 1997.
20. C. Liverani, B. Saussol and S. Vaienti. Conformal measure and decay of correlations for covering weighted systems. Ergod. Th. & Dynam. Sys. 18(6) (1998), 1399-1420.
21. C. Liverani, B. Saussol and S. Vaienti. A probabilistic approach to intermitency. Ergod. Th. & Dynam. Sys. 19(3) (1999), 671-685.
22. V. Maume-Deschamps. Propriétés de mélange pour des systèmes dynamiques markoviens. Ph.D. thesis, Université de Bourgogne, 1998, http://www.u-bourgogne.fr/monge/v.maume/accueil.html.
23. M. Mori. On the intermitency of a piecewise linear map (Takahashi model). Tokyo J. Math. 16(2) (1993), 411-428.
24. F. Paccaut. Statistics of return times for weighted maps of the interval. Ann. Inst. Poincaré Sec. Prob. Stat. to appear.
25. O. Sarig. Thermodynamic formalism for countable Markov shifts. Ergod. Th. & Dynam. Sys. 19(6) (1999), 1565-1593.
26. B. Saussol. Étude statistique de systèmes dynamiques dilatants. Ph.D. thesis, Université de Toulon.
27. M. Thaler. Estimates of the invariant densities of endomorphisms with indifferent fixed point. Israel J. Math. 37 (1980), 303-314.
28. M. Viana. Stochastic Dynamics of Deterministic Systems (Brazilian Math. Colloquium, IMPA), 1997.
29. X. J. Wang. Statistical physics of temporal intermitency. Phys. Rev. A 40 (1989), 6647.
30. L.-S. Young. Recurrence times and rates of mixing. Israel J. Math. 110 (1999), 153-188.