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Lyapunov exponents for random perturbations of some area-preserving maps including the standard map. (English) Zbl 1365.37039
This paper studies a class of area-preserving diffeomorphisms which are not uniformly hyperbolic and includes the standard map. The authors show that by having a small independent random perturbation at each iteration, the resulting maps have positive Lyapunov exponent. Z. Lian and M. Stenlund [Dyn. Syst. 27, No. 2, 239–252 (2012; Zbl 1293.37023)] obtained an analogous one-dimensional result.

MSC:
37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37H15 Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents
Citations:
Zbl 1293.37023
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