Geodesic
Lyapunov exponents for random perturbations of some area-preserving maps including the standard map
Alex Blumenthal1 ; Jinxin Xue2 ; Lai-Sang Young1
1 Courant Institute of Mathematical Sciences, New York University, New York, NY
2 University of Chicago, Chicago, IL
Annals of mathematics, Tome 185 (2017) no. 1, pp. 285-310.

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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.
DOI : 10.4007/annals.2017.185.1.5

Alex Blumenthal 1 ; Jinxin Xue 2 ; Lai-Sang Young 1

1 Courant Institute of Mathematical Sciences, New York University, New York, NY
2 University of Chicago, Chicago, IL 
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Alex Blumenthal; Jinxin Xue; Lai-Sang Young. Lyapunov exponents for random perturbations of some area-preserving maps including the standard map. Annals of mathematics, Tome 185 (2017) no. 1, pp. 285-310. doi : 10.4007/annals.2017.185.1.5. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.1.5/

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