Equilibrium states and invariant measures for random dynamical systems

Details Equilibrium states and invariant measures for random dynamical systems Equilibrium states and invariant measures for random dynamical systems

2012-03-29

arxiv.org/abs/1203.6432v1

Mathematics

Dynamical Systems

22 pages

Scientific paper

The existence of invariant Borel probability measures for random dynamical systems on complete metric spaces is proved under assumptions that the systems have countably many maps and admit finite Markov partitions such that the resulting Markov systems are uniformly continuous and contractive, and satisfy some integrability condition in the infinite case. A one-to-one map between these measures and equilibrium states associated with such systems is established. Some properties of the map and the measures are given.

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