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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