Smooth Ergodic Theory of Random Dynamical Systems

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This text studies ergodic-theoretic aspects of random dynamical systems, for example, deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems. An entropy formula of Pesin’s type occupies the central part of the text whilst chapter two introduces relation numbers highlighting canonical methods in dynamical systems and measure theory. The text is intended for readers interested in noise-perturbed dynamical systems and may indicate further areas of study. Reasonable knowledge of differetial geometry, measure theory, ergodic theory, dynamical systems and preferably random processees is assumed.