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Ruelle's transfer operator for random subshifts of finite type

Published online by Cambridge University Press:  19 September 2008

Thomas Bogenschütz  and
Volker Mathias Gundlach
Thomas Bogenschütz
Affiliation:
Institut für Dynamische Systeme, Universität Bremen, Postfach 330440, 28334 Bremen, Germany
Volker Mathias Gundlach
Affiliation:
Institut für Dynamische Systeme, Universität Bremen, Postfach 330440, 28334 Bremen, Germany
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Abstract

We consider a Ruelle—Perron—Frobenius type of selection procedure for probability measures that are invariant under random subshifts of finite type. In particular we prove that for a class of random functions this method leads to a unique probability exhibiting properties that justify the names Gibbs measure and equilibrium states. In order to do this we introduce the notion of bundle random dynamical systems and provide a theory for their invariant measures as well as give a precise definition of Gibbs measures.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 3 , June 1995 , pp. 413 - 447
Copyright
Copyright © Cambridge University Press 1995

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