Projective metrics and mixing properties on towers

Transactions of the American Mathematical Society

Volumn 353, Issue 8, 2001, Pages 3371-3389

  Maume Deschamps, Véronique ^a,b  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b UNIVERSITÉ DE BOURGOGNE   (France)

Author keywords

Decay of correlations; Projective metrics; Tower; Transfer operator

Indexed keywords

EID: 23044528342     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-01-02786-6     Document Type: Article

References (30)

1. [A,D,U] J. AARONSON, M. DENKER, and M. URBANSKI Ergodic theory for Markov fibered systems and parabolic rational maps. Trans. Amer. Math. Soc. (1993), 337 (2), 495-548MR 94g:58116
2. [Ba,V] V. BALADI, M. VIANA Strong stochastic stability and rate of mixing for unimodal maps. Ann. Sci. École Norm. Sup. (1996) 29, 4, 483-517MR 97d:58170
3. [Ba,Y] V.BALADI, L.-S. YOUNG On the spectra of randomly perturbed expanding maps. Comm. Math. Phys. (1993) 156, 2, 355-385MR 94g:58172
4. [B,Y] M. BENEDICKS and L.-S. YOUNG Decay of correlations for certain Henon maps. (1996) preprint.
5. [Bi1] G. BIRKHOFF Extensions of Jentzch's theorem. T.A.M.S. (1957), 85, 219-227MR 19:296a
6. [Bi2] G. BIRKHOFF Lattice theory (3rd edition). Amer. Math. Soc. (1967)MR 37:2635
7. [Buz] J. BUZZI Markov extensions for multi-dimensional dynamical systems. Israel J. Math. 112 (1999), 357-380MR 2000m:37008
8. [Ca] A.A. CASTRO Backward inducing and exponential decay of correlations for partially hyperbolic attractors with mostly contracting central direction. PhD Thesis (1998).
9. P. COLLET Statistics of closest return for some non uniformly hyperbolic systems. Preprint (1999)
10. [C,G,S] P. COLLET, A. GALVES, B. SCHMITT Unpredictability of the occurrence time of a long laminar period in a model of temporal intermitency. Ann. Inst. H. Poincaré Phys. Théor. (1992), 57, 3, 319-331MR 94a:58064
11. [Ch] N. CHERNOV Statistical properties of piecewise smooth hyperbolic systems in high dimensions. Discrete Contin. Dynam. Systems (1999), 5, 2, 425-448MR 99k:58134
12. D. DOLGOPYAT On dynamics of mostly contracting diffeomorphisms. Preprint (1998).
13. [F,S1] P. FERRERO, B. SCHMITT Ruelle Perron Frobenius theorems and projective metrics. Colloque Math. Soc. J. Bolyai Random Fields. Estergom (Hungary) (1979).
14. [F,S2] P. FERRERO, B. SCHMITT On the rate of convergence for some limit ratio theorems related to endomorphisms with a non regular invariant density. Preprint (1994).
15. [G,S] A. GALVES & B. SCHMITT Inequalities for hitting time in mixing dynamical systems. Random and Computational Dynamics (1997), 5, 4, 337-347MR 98i:60017
16. [H] F. HOFBAUER On intrinsic ergodicity of piecewise monotonie transformations with positive entropy. Israel J. Math. (1979), 34, 1, 213-237;
17. (1981), 38, 11, 107-115.
18. [K,N] G. KELLER, T. NOWICKI Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps. Comm. Math. Phys. (1992), 149, 1, 31-69MR 93i:58123
19. [K,M,S] A. KONDAH, V. MAUME, and B. SCHMITT Vitesse de convergence vers l'état d'équlibre pour des dynamiques markoviennes non höldériennes. Ann. Inst. Poincarré Sec. Prob. Stat. (1997) 33 (6) 675-695MR 99e:28032
20. [Li1] C. LIVERANI Decay of correlations. Ann. of Math. (1995), 142 (2), 239-301MR 96e:58090
21. [Li2] C. LIVERANI Central limit theorem for deterministic systems. Proceedings of the International Congress on Dynamical Systems, Montevideo 95, Research Notes in Mathematics series, Pittman, (1997)MR 98k:28025
22. [Ma1] V. MAUME-DESCHAMPS Propriétés de mélange pour des systèmes dynamiques markoviens. PhD Thesis, Université de Bourgogne (1998), http://www.u-bourgogne.fr/ monge/v.maume/accueil.html.
23. [Ma2] V. MAUME-DESCHAMPS Correlation decay for Markov maps on a countable state space. To appear in Erg. Th Dyn. Syst.
24. [P] F. PACCAUT Statistics of return times for weighted maps of the interval Prcprint (1999).
25. [Sa] O. SARIG Thermodynamic Formalism for Countable Markov Shifts. 19 (1999), 1565-1593MR 2000m:37009
26. [Sau] B. SAUSSOL Étude statistique de systèmes dynamiques dilatants. PhD. Thesis, Université de Toulon.
27. [Se] E. SENETA Non-negative matrices and Markov chains. Springer (1981)MR 85i:60058
28. M. VIANA Stochastic dynamics of deterministic systems. (1997).
29. [Yl] L.-S. YOUNG Statistical properties of dynamical systems with some hyperbolicity. Ann. of Math. (2) (1998), 147, 3, 585-650MR 99h:58140
30. [Y2] L.-S. YOUNG Recurrence times and rates of mixing. Israel J. Math. 110 (1999), 153-188. CMP 2000:11