Lyapunov exponents for random perturbations of some area-preserving maps including the standard map

Abstract

We consider a large class of 2D area-preserving diffeomorphisms that are not uniformly hyperbolic but have strong hyperbolicity properties on large regions of their phase spaces. A prime example is the Standard map. Lower bounds for Lyapunov exponents of such systems are very hard to estimate, due to the potential switching of "stable" and "unstable" directions. This paper shows that with the addition of (very) small random perturbations, one obtains with relative ease Lyapunov exponents reflecting the geometry of the deterministic maps.

19 pages

References in corpus (2)

• Continuity of Lyapunov Exponents for Random 2D Matrices
• Bounds on the Lyapunov exponent via crude estimates on the density of states

Cited by in corpus (3)

• Uniqueness of the measure of maximal entropy for the standard map
• Hilbert Space Lyapunov Exponent stability
• Statistical properties for compositions of standard maps with increasing coefficent