Isomorphic random Bernoulli shifts

• Autorzy: V. M. Gundlach , G. Ochs
• Języki publikacji: EN

Abstrakty

EN

We develop a relative isomorphism theory for random Bernoulli shifts by showing that any random Bernoulli shifts are relatively isomorphic if and only if they have the same fibre entropy. This allows the identification of random Bernoulli shifts with standard Bernoulli shifts.

Słowa kluczowe

EN

fibre entropy; random dynamical system; random shift; relative isomorphism

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 84/85
• Numer: 2
• Strony: 327-344

Daty

wydano

2000

otrzymano

1999-08-11

poprawiono

2000-02-01

Twórcy

autor

V. M. Gundlach

• Institut für Dynamische Systeme, Universität Bremen, Postfach 330 440, 28334 Bremen, Germany

autor

G. Ochs

• Institut für Dynamische Systeme, Universität Bremen, Postfach 330 440, 28334 Bremen, Germany

Bibliografia

• [Bog93] T. Bogenschütz, Equilibrium states for random dynamical systems, PhD thesis, Universität Bremen, 1993.
• [BG92] T. Bogenschütz and V. M. Gundlach, Symbolic dynamics for expanding random dynamical systems, Random Comput. Dynamics 1 (1992), 219-227.
• [Con97] N. D. Cong, Topological Dynamics of Random Dynamical Systems, Clarendon Press, Oxford, 1997.
• [CFS82] I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai, Ergodic Theory, Grundlehren Math. Wiss. 245, Springer, New York, 1982.
• [Gun99] V. M. Gundlach, Random shifts and matrix products, Habilitationsschrift, 1999.
• [GK99] V. M. Gundlach and Y. Kifer, Random hyperbolic systems, in: H. Crauel and V. M. Gundlach (eds.), Stochastic Dynamics, Berlin, Springer, 1999, 117-145.
• [Kie84] J. Kieffer, A simple development of the Thouvenot relative isomorphism theory, Ann. Probab. 12 (1984), 204-211.
• [Kif86] Y. Kifer, Ergodic Theory of Random Transformations, Birkhäuser, Boston, 1986.
• [Kif96] Y. Kifer, Fractal dimensions and random transformations, Trans. Amer. Math. Soc. 348 (1996), 2003-2038.
• [Lin77] D. A. Lind, The structure of skew products with ergodic group automorphisms, Israel J. Math. 28 (1977), 205-248.
• [Orn70] D. Ornstein, Bernoulli shifts with the same entropy are isomorphic, Adv. Math. 4 (1970), 337-352.
• [Pet83] K. Petersen, Ergodic Theory, Cambridge Univ. Press, Cambridge, 1983.
• [Rah78] M. Rahe, Relatively finitely determined implies relatively very weak Bernoulli, Canad. J. Math. 30 (1978), 531-548.
• [Shi77] P. Shields, Weak and very weak Bernoulli partitions, Monatsh. Math. 84 (1977), 133-142.
• [Th75a] J.-P. Thouvenot, Quelques propriétés des systèmes dynamiques qui se décomposent en un produit de deux systèmes dont l'un est un schéma de Bernoulli, Israel J. Math. 21 (1975), 177-207.
• [Th75b] J.-P. Thouvenot, Remarques sur les systèmes dynamiques donnés avec plusieurs facteurs, ibid., 215-232.