Random hyperbolic systems

VM Gundlach; Y Kifer

doi:10.1007/0-387-22655-9_6

Random hyperbolic systems

VM Gundlach
, Y Kifer

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We review definitions of random hyperbolic sets and introduce a characterization using random cones. Moreover we discuss problems connected with symbolic representations and the thermodynamic formalism for random hyperbolic systems both in discrete and continuous time cases. In the discrete time case we prove the existence of Markov partitions to guarantee symbolic dynamics and the existence of SRB-measures, while in the continuous time case we explain why a respective method does not work. We illustrate the theory with a number of examples.

Original language	English
Title of host publication	Stochastic Dynamics
Editors	H Crauel, M Gundlach
Publisher	Springer
Pages	117-145
Number of pages	29
DOIs	https://doi.org/10.1007/0-387-22655-9_6
State	Published - 1999

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10.1007/0-387-22655-9_6

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title = "Random hyperbolic systems",

abstract = "We review definitions of random hyperbolic sets and introduce a characterization using random cones. Moreover we discuss problems connected with symbolic representations and the thermodynamic formalism for random hyperbolic systems both in discrete and continuous time cases. In the discrete time case we prove the existence of Markov partitions to guarantee symbolic dynamics and the existence of SRB-measures, while in the continuous time case we explain why a respective method does not work. We illustrate the theory with a number of examples.",

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Random hyperbolic systems

Abstract

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