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Lyapunov exponents for random perturbations of coupled standard maps. (English) Zbl 1527.37035

Summary: In this paper, we give a quantitative estimate for the first \(N\) Lyapunov exponents for random perturbations of a natural class of \(2N\)-dimensional volume-preserving systems exhibiting strong hyperbolicity on a large but noninvariant subset of the phase space. Concrete models covered by our setting include systems of coupled standard maps, in both ‘weak’ and ‘strong’ coupling regimes.

MSC:

37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D05 Dynamical systems with hyperbolic orbits and sets
37A05 Dynamical aspects of measure-preserving transformations
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