On the convergence to equilibrium states for certain non-hyperbolic systems

Ergodic Theory and Dynamical Systems

Volumn 17, Issue 4, 1997, Pages 977-1000

  Yuri, Michiko ^a  

^a Sapporo University   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031495876     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385797086240     Document Type: Article

References (36)

1. J. Aaronson. Ergodic theory for inner functions of the upper half plane. Ann. inst. H. Poincare. 14 (1978), 233-253.
2. J. Aaronson, M. Denker and M. Urbanski. Ergodic theory for Markov fibered systems and parabolic rational maps. Trans. Amer. Math. Soc. 337 (1993), 495-548.
3. R. L. Adler. F-expansions revisited. Recent Advances in Topological Dynamics (1-5). Springer, New York, 1975.
4. P. Billingsley. Ergodic Theory and Information. Wiley, New York, 1965.
5. R. Bowen. Invariant measures for Markov maps of the interval. Comm. Math. Physics. 69 (1979), 1-17.
6. M. Denker and M. Urbanski. Ergodic theory of equilibrium states for rational maps. Nonlinearity 4 (1991), 103-134.
7. M. Denker and M. Urbanski. On the existence of conformal measures. Trans. Amer. Math. Soc. 328 (1991), 563-587.
8. S. Ito and M. Yuri. Number theoretical transformations with finite range structure and their ergodic properties. Tokyo J. Math. 10 (1987), 1-32.
9. F. Ledrappier. Some properties of absolutely continuous invariant measures on an interval. Ergod. Th. & Dynam. Sys. 1 (1981), 77-93.
10. M. Lin. Mixing for Markov operators. Z. Wahrsch. Verw. Gebiete. 19 (1971), 231-243.
11. A. Lasota and J. A. Yorke. On the existence of invariant measures for piecewise monotonic transformations. Trans. Amer. Math. Soc. 186 (1973) 481-488.
12. H. Nakada. On the Kuzmin's theorem for complex continued fractions. Keio Engrg. Rep. 29 (1976), 93-108.
13. M. Pollicott and M. Yuri. Regularity of the solutions to measurable Livsic equation. Preprint.
14. A. Renyi. Representations for real numbers and their ergodic properties. Acta. Math. Acad. Sc. Hungar. 8 (1957), 477-493.
15. D. Ruelle. Statistical mechanics of a one-dimensional lattice gas. Comm. Math. Phys. 9 (1968), 267-278.
16. D. Ruelle. Thermodynamic Formalism (Encycl. Math. Appel. 5). Addison-Wesley, 1978.
17. D. Ruelle. Repellers for real analytic maps. Ergod. Th. & Dynam. Sys. 2 (1982), 99-107.
18. F. Schweiger. Some remarks on ergodicity and invariant measures. Michigan Math. J. 22 (1975), 181-187.
19. F. Schweiger. Number theoretical endomorphisms with σ-finite invariant measure. Israel J. Math 21 (1975), 308-318.
20. F. Schweiger. Ergodic Theory of Fibred Systems and Metric Number Theory. Oxford University Press, 1995.
21. F. Schweiger and M. Waterman. Some remarks on Kuzmin's theorem for F-expansions. J. Number Th. 5 (1973), 123-131.
22. Y. G. Sinai. Markov partitions and C-diffeomorphisms. Anal. and Appl. 2 (1968), 70-80.
23. S. Tanaka. A complex continued fraction transformation and its ergodic properties. Tokyo J. Math. 8 (1985), 191-214.
24. M. Thaler. Estimates of the invariant densities of endomorphisms with indifferent fixed points. Israel J. Math. 37 (1980), 303-315.
25. M. Thaler. Transformations on [0, 1] with infinite invariant measures. Israel J. Math. 46 (1983), 67-97.
26. M.Thaler. A limit theorem for the Perron Frobenius operator of transformations on [0, 1] with indifferent fixed points. Israel J. Math. 91 (1995), 111-129.
27. P. Walters. Invariant measures and equilibrium states for some mappings which expand distances. Trans. Amer. Math. Soc. 236 (1978), 121-151.
28. M. S. Waterman. Some ergodic properties of multi-dimensional f-expansions. Z. Wahrsch. Verw. Gebiete. 16 (1971), 77-103.
29. M. Yacobson. Topological and metric properties of one-dimensional endomorphisms. Dokl. Akad. Nauk USSR. 243 (1978), 866-869.
30. M. Yuri. On a Bernoulli property for multi-dimensional maps with finite range structure. Tokyo J. Math. 9 (1986), 457-485.
31. M. Yuri. Invariant measures for certain multi-dimensional maps. Nonlinearity 7 (1994), 1093-1124.
32. M. Yuri. Multi-dimensional maps with infinite invariant measures and countable state sofic shifts. Indagationes Mathematicae 6 (1995), 355-383.
33. M. Yuri. Zeta functions for certain nonhyperbolic systems and topological Markov approximations. To appear in Ergod. Th. & Dynam. Sys..
34. M. Yuri. Some remarks on invariant densities for certain nonhyperbolic system. Preprint.
35. M. Yuri. Decay of correlations for certain multi-dimensional maps. Nonlinearity 9 (1996), 1439-1461.
36. M. Yuri. Statistical properties for nonhyperbolic maps with finite range structure. Preprint.