An invariance principle for maps with polynomial decay of correlations

Communications in Mathematical Physics

Volumn 260, Issue 1, 2005, Pages 1-15

  Tyran Kamińska, Marta ^a  

^a UNIVERSITY OF SILESIA   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 25444440569     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1400-z     Document Type: Article

References (43)

1. Adler, R., Rivlin, T.: Ergodic and mixing properties of Chebyshev polynomials. Proc. Amer. Math. Soc. 15, 794-796 (1964)
2. Baladi, V.: Positive Transfer Operators and Decay of Correlations. Volume 16 of Advanced Series in Nonlinear Dynamics. River Edge, NJ: World Scientific Publishing Co. Inc., 2000
3. Billingsley, P.: Convergence of Probability Measures. John Wiley & Sons, New York, 1968
4. Billingsley, P.: Probability and Measure. New York: John Wiley & Sons, 1995
5. Bowen, R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Volume 470 of Lecture Notes in Math., New York: Springer-Verlag, 1975
6. Bruin, H., Luzzatto, S., Van Strien, S.: Decay of correlations in one-dimensional dynamics. Ann. Sci. École Norm. Sup. (4), 36, 621-646 (2003)
7. Bruin, H., Vaienti, S.: Return time statistics for unimodal maps. Fund. Math., 176, 77-94 (2003)
8. Butzer, P.L., Westphal, U.: The mean ergodic theorem and saturation. Indiana Univ. Math. J. 20, 1163-1174 (1970/1971)
9. Chernov, N.: Limit theorems and Markov approximations for chaotic dynamical systems. Probab. Theory Relat. Fields 101, 321-362 (1995)
10. Conze, J.-P., Le Borgne, S.: Méthode de martingales et flot géodésique sur une surface de courbure constante négative. Ergodic Theory Dynam. Systems 21, 421-441 (2001)
11. Denker, M.: The central limit theorem for dynamical systems. In: Dynamical systems and ergodic theory (Warsaw, 1986), Volume 23 of Banach Center Publ. Warsaw: PWN, 1989 pp. 33-62
12. Derriennic, Y., Lin, M.: The central limit theorem for Markov chains with normal transitions started at a point. Probab. Theory Relat. Fields 119, 508-528 (2001a)
13. Derriennic, Y., Lin, M.: Fractional Poisson equation and ergodic theorems for fractional coboundaries. Israel J. Math. 123, 93-130 (2001b)
14. Derriennic, Y. and Lin, M.: The central limit theorem for Markov chains a point. Probab. Theory Relat. Fields 125, 73-76 (2003)
15. Dolgopyat, D.: On mixing properties of compact group extensions of hyperbolic systems. Israel J. Math. 130, 157-205 (2002)
16. Dolgopyat, D.: Limit theorems for partially hyperbolic systems. Trans. Amer. Math. Soc. 356(4), 1637-1689 (2004)
17. Eagleson, G.K.: Martingale convergence to mixtures of infinitely divisible laws. Ann. Probab. 3, 557-562 (1975)
18. Fan, A., Jiang, Y.: On Ruelle-Perron-Frobenius operators. I. Ruelle theorem. Comm. Math. Phys. 223, 125-141 (2001a)
19. Fan, A., Jiang, Y.: On Ruelle-Perron-Frobenius operators. II. Convergence speeds. Comm. Math. Phys. 223, 143-159 (2001b)
20. Field, M., Melbourne, I., Török. A.: Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions. Ergodic Theory Dynam. Systems 23(1), 87-110 (2003)
21. Gordin, M.I.: The central limit theorem for stationary processes. Dokl. Akad. Nauk SSSR 188, 739-741 (1969)
22. Gouëzel, S.: Central limit theorem and stable laws for intermittent maps. Probab. Theory Related Fields 128, 82-122 (2004a)
23. Gouëzel, S.: Sharp polynomial estimates for the decay of correlations. Israel J. Math. 139, 29-65 (2004b)
24. Hilgers, A., Beck, C: Higher-order correlations of Tchebyscheff maps. Physica D 156, 1-18 (2001)
25. Hofbauer, F., Keller, G.: Ergodic properties of invariant measures for piecewise monotonic transformations. Math. Z. 180, 119-140 (1982)
26. Hu, H.: Decay of correlations for piecewise smooth maps with indifferent fixed points. Ergodic Theory Dynam. Systems 24(2), 495-524 (2004)
27. Isola, S.: Renewal sequences and intermittency. J. Statist. Phys. 97, 263-280 (1999)
28. Keller, G.: Un théorème de la limite centrale pour une classe de transformations monotones par morceaux. C.R. Acad. Sc. Paris 291, 155-158 (1980)
29. Liverani, C.: Decay of correlations. Ann. of Math. (2) 142, 239-301 (1995)
30. Liverani, C.: Central limit theorem for deterministic systems. In: International Conference on Dynamical Systems (Montevideo, 1995), Volume 362 of Pitman Res. Notes Math. Ser. Harlow: Longman, 1996, pp. 56-75
31. Liverani, C., Saussol, B., Vaienti, S.: A probabilistic approach to intermittency. Ergodic Theory Dynam. Systems 19, 671-685 (1999)
32. Mackey, M.C., Tyran-Kamińska, M.: Deterministic Brownian motion: The effects of perturbing a dynamical system by a chaotic semi-dynamical system. Preprint, 2004
33. Maume-Deschamps, V.: Projective metrics and mixing properties on towers. Trans. Amer. Math. Soc. 353, 3371-3389 (2001)
34. Maxwell, M., Woodroofe, M.: Central limit theorems for additive functional of Markov chains. Ann. Probab. 28, 713-724 (2000)
35. Melbourne, I., Török, A.: Central limit theorems and invariance principles for time-one maps of hyperbolic flows. Commun. Math. Phys. 229, 57-71 (2002)
36. Pollicott, M.: Rates of mixing for potentials of summable variation. Trans. Amer. Math. Soc. 352, 843-853 (2000)
37. Pollicott, M., Sharp, R.: Invariance principles for interval maps with an indifferent fixed point. Commun. Math. Phys. 229, 337-346 (2002)
38. Sarig, O.: Subexponential decay of correlations. Invent. Math. 150, 629-653 (2002)
39. Sinai, Y.G.: Gibbs measure in ergodic theory. Russian Math. Surveys 27, 21-69 (1972)
40. Viana, M.: Stochastic dynamics of deterministic systems. Col. Bras, de Matemática 21, 197 (1997)
41. Young, L.-S.: Statistical properties of dynamical systems with some hyperbolicity. Ann. of Math. (2) 147, 585-650 (1998)
42. Young, L.-S.: Recurrence times and rates of mixing. Israel J. Math. 110, 153-188 (1999)
43. Zweimüller, R.: Stable limits for probability preserving maps with indifferent fixed points. Stoch. Dyn. 3(1), 83-99 (2003)