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Conservativity of random Markov fibred systems

Published online by Cambridge University Press:  01 February 2008

MANFRED DENKER ,
YURI KIFER  and
MANUEL STADLBAUER
MANFRED DENKER
Affiliation:
Institut für Mathematische Stochastik, Maschmühlenweg 8-10, 37073 Göttingen, Germany (email: denker@math.uni-goettingen.de, stadelba@math.uni-goettingen.de)
YURI KIFER
Affiliation:
Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel (email: kifer@math.huji.ac.il)
MANUEL STADLBAUER
Affiliation:
Institut für Mathematische Stochastik, Maschmühlenweg 8-10, 37073 Göttingen, Germany (email: denker@math.uni-goettingen.de, stadelba@math.uni-goettingen.de)
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Abstract

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In this paper we extend results concerning conservativity and the existence of σ-finite measures to random transformations which admit a countable relative Markov partition. We consider random systems which are locally fibre-preserving and which admit a countable, relative Markov partition. If the system is relative irreducible and satisfies a relative distortion property we deduce that the system is either totally dissipative or conservative and ergodic. For conservative systems, we provide sufficient conditions for the existence of absolutely continuous σ-finite invariant measures.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 1 , February 2008 , pp. 67 - 85
Copyright
Copyright © Cambridge University Press 2007

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