Expansiveness, specification, and equilibrium states for random bundle transformations

Discrete and Continuous Dynamical Systems

Volumn 6, Issue 1, 2000, Pages 89-120

  Gundlach, V M ^a   Kifer, Yu ^b  

^a UNIVERSITY OF BREMEN   (Germany)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Equilibrium states; Gibbs states; Random shifts; Random transformations

Indexed keywords

EID: 0034380910     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. L. Arnold. Random Dynamical Systems. Springer-Verlag, New York, Berlin, 1998.
2. L.M. Abramov and V.A. Rohlin. The entropy of a skew product of measure-preserving transformation. Amer. Math. Soc. Transl. Ser.2, 48 (1966), 255-265.
3. V. Baladi. Gibbs states and equilibrium states for finitely presented dynamical systems. Jour. Stat. Phys., 62 (1991), 239-256.
4. T. Bogenschütz and V.M. Gundlach. Ruelle's transfer operator for random subshifts of finite type. Ergod. Th. & Dynam. Sys., 15 (1995), 413-447.
5. T. Bogenschütz. Entropy, pressure, and a variational principle for random dynamical systems. Random & Computational Dynamics, 1 (1992), 99-116.
6. R. Bowen. Some systems with unique equilibrium states. Math. Systems Theory, 8 (1974), 193-202.
7. R. Bowen. Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math. 470 Springer, New York, Berlin, 1975.
8. v-action. Commun. Math. Phys., 48 (1976), 85-88.
9. C. Castaing and M. Valadier. Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580 Springer, New York, Berlin, 1977.
10. R.M. Dudley. Real Analysis and Probability, Wadsworth & Brooks, Pacific Grove, 1989.
11. V.M. Gundlach and Y. Kifer. Random hyperbolic systems, in: Stochastic Dynamics (H. Crauel and M. Gundlach eds.), Springer-Verlag, New York 1999, p.p. 117-145.
12. N. Haydn and D. Ruelle. Equivalence of Gibbs and equilibrium states for homeomorphisms satisfying expansiveness and specification. Comm. Math. Phys., 148 (1992), 155-167.
13. Y. Kifer. Ergodic Theory of Random Transformations. Birkhäuser, Boston, 1986.
14. Y. Kifer. Large deviations in dynamical systems and stochastic processes. Trans. Amer. Math. Soc., 321 (1990), 505-524.
15. Y. Kifer. Equilibrium states for random expanding transformations. Random & Computational Dynamics, 1 (1992), 1-31.
16. Y. Kifer. Fractal dimensions and random transformations. Trans. Amer. Math. Soc., 348 (1996), 2003-2038.
17. d - Actions, LMS Lect. Note Ser., vol. 228, 415-432, Cambridge Univ. Press, Cambridge, 1996.
18. Y. Kifer. On the topological pressure for random bundle transformations. In V. Turaev and A. Vershik ed., Rohlin's memorial volume, Adv. Math. Studies, Amer. Math. Soc. 2000.
19. K. Khanin and Y. Kifer. Thermodynamic formalism for random transformations and statistical mechanics. In L.A. Bunimovich, B.M. Gurevich, Ya.B. Pesin ed. Sinai's Moscow Seminar on Dynamical Systems, Amer. Math. Soc. Transl. Ser. 2, 171 (1996), 107-140.
20. R. Kenyon and Y. Peres. Hausdorff dimensions of sofic affine-invariant sets. Israel J. Math., 94 (1996), 157-178.
21. F. Ledrappier and P. Walters. A relativized variational principle for continuous transformations. J. London Math. Soc. (2), 16 (1977), 568-576.
22. P.-D. Liu. Random perturbations of Axiom A sets. Jour. Stat. Phys., 90 91998), 467-490.
23. D. Lind and B. Marcus. An Introduction to Symbolic Dynamics and Coding. Cambridge Univ. Press, Cambridge, 1995.
24. V.A. Rohlin. Selected topics from the metric theory of dynamical systems. Amer. Math. Soc. Transl. Ser.2, 49 (1966), 171-240.
25. v-action satisfying expansiveness and specification. Trans. Amer. Math. Soc., 185 (1972), 237-251.
26. D. Ruelle. Thermodynamic Formalism, volume 5 of Encyclopedia of Mathematics and its Applications. Addison-Wesley, Reading, Mass., 1978.
27. D. Ruelle. Thermodynamic formalism for maps satisfying positive expansiveness and specification. Nonlinearity, 5 (1992), 1223-1236.
28. Ya.G. Sinai. Gibbs measures in ergodic theory. Russian Math. Surveys, 4 91972), 21-69.
29. P. Walters. An Introduction to Ergodic Theory Springer-Verlag, New York, 1982.
30. B. Weiss. Subshifts of Finite Type and Sofic Systems Monat. Math., 77 (1973), 462-474.