Expansiveness, specification, and equilibrium states for random bundle transformations

V. M. Gundlach; Yu. Kifer

doi:10.3934/dcds.2000.6.89

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2000, Volume 6, Issue 1: 89-120. Doi: 10.3934/dcds.2000.6.89

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Expansiveness, specification, and equilibrium states for random bundle transformations

V. M. Gundlach^1, and
Yu. Kifer^2,

1.
Institut für Dynamische Systeme, Universität Bremen, 28334 Bremen
2.
Institute of Mathematics, The Hebrew University, Jerusalem 91904

Received: September 30, 1999

Published: December 1999

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Abstract

We introduce notions of expansiveness, conjugation, and specification for random bundle transformations and derive the uniqueness of equilibrium states for a large class of functions. We consider both invertible and noninvertible cases and discuss the results in the random subshifts case. As an example of such systems we introduce random sofic shifts which can be described both via random graphs and as factors of random subshifts of finite type. Based on the random graph description we discuss large deviation results for random sofic shifts.

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Mathematics Subject Classification: Primary: 58F03, 58F11; Secondary: 28D20, 60J05, 82B44.

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