Non-ergodicity for C1 expanding maps and g-measures

Ergodic Theory and Dynamical Systems

Volumn 16, Issue 3, 1996, Pages 531-543

  Quas, Anthony N ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030554839     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0143385700008956     Document Type: Article

References (23)

1. H. Berbee. Chains with infinite connections, uniqueness and Markov representation. Probab. Th. Rel. Fields 76 (1987), 243-253.
2. C. J. Bose. Generalized baker's transformations. Ergod. Th. & Dynam. Sys. 9 (1989), 1-17.
3. A. Boyarsky and W. Byers. A graph-theoretic bound on the number of independent absolutely continuous invariant measures. J. Math. Anal. Appl. 139 (1989), 139-151.
4. A. Boyarsky and M. Scarowsky, On a class of transformations which have unique absolutely continuous invariant measure. Trans. Amer. Math. Soc. 255 (1979), 243-262.
5. M. Bramson and S. A. Kalikow. Nonuniqueness in g-functions. Israel J. Math. 84 (1993), 153-160.
6. W. Doeblin and R. Fortet. Sur les chaînes à liaisons complètes. Bull. Soc. Math. France 65 (1937), 132-148.
7. 1 par morceaux de l'intervalle, sans probabilité absolument continue invariante. Ergod. Th. & Dynam. Sys. 9 (1989), 101-113.
8. P. Hulse. Uniqueness and ergodic properties of ergodic g-measures. Ergod. Th. & Dynam. Sys. 11 (1991), 65-77.
9. T. Kaijser. On a theorem of Karlin. Preprint. Department of Electrical Engineering, Linköping University, Sweden, 1993.
10. S. A. Kalikow. Random Markov processes and uniform martingales. Israel J. Math. 71 (1990), 33-54.
11. S. Karlin. Some random walks arising in learning models, 1. Pac. J. Math. 3 (1953), 725-756.
12. M. Keane. Strongly mixing g-measures. Invent. Math. 16 (1972), 309-324.
13. Z. S. Kowalski. Invariant measures for piecewise monotonic transformations. Proc. Winter School of Probability (Karpacz, 1975). Springer Lecture Notes in Mathematics 472 (1975), 77-94.
14. K. Krzyżewski. On expanding mappings. Bull. Acad. Polon. Sci. Sér. Sci. Math. XIX (1971), 23-24.
15. K. Krzyżewski. A remark on expanding mappings. Colloq. Math. XLI (1979), 291-295.
16. K. Krzyżewski and W. Szlenk. On invariant measures for expanding differentiable mappings. Studia Math. XXXIII (1969), 83-92.
17. A. Lasota and J. A. Yorke. On the existence of invariant measures for piecewise monotonic transformations. Trans. Amer. Math. Soc. 186 (1973), 481-488.
18. T. Y. Li and J. A. Yorke. Ergodic transformations from an interval into itself. Trans. Amer. Math. Soc. 235 (1978), 183-192.
19. T. Lindvall. Lectures on the Coupling Method. Wiley, New York, 1992.
20. R. Mañé. Ergodic Theory and Differentiable Dynamics. Springer, New York, 1988.
21. A. N. Quas. Some problems in ergodic theory. Thesis, University of Warwick, 1993.
22. P. Walters. Ruelle's operator theorem and g-measures. Trans. Amer. Math. Soc. 214 (1975), 375-387.
23. S. Wong. Some metric properties of piecewise monotonic mappings of the unit interval. Trans. Amer. Math. Soc. 246 (1978), 493-500.