Abstract
This chapter discusses random dynamical systems (RDS). The theory of random perturbations of dynamical systems deals either with discrete time models where each iteration of a deterministic transformation F is followed by a small noise (which can be chosen in various ways) that amounts to a Markov chain. Lyapunov exponents and entropy provide two different ways of measuring the dynamical complexity of RDS. The Lyapunov exponents measure geometrically how fast nearby orbits diverge (due to the corresponding invariant manifolds theory) or how fast volume elements are expanded (by sums of the exponents), and the entropy measures from the point of view of the information the complexity related to such dynamical behaviors. Furthermore, Markov chains with random transition probabilities are both ideologically close to RDS and emerge directly in the study of random Markov subshifts of finite type.
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