2017/01/26 by Alex Blumenthal, Jinxin Xue, Lai-Sang Young · 1 citation
Mathematics · #math.DS #msc:37D25 #msc:37H15
paper · pdf · doi:10.4007/annals.2017.185.1.5
published as Annals of Mathematics 185.1: 285-310 (2017) · 19 pages
arxiv created 2017/01/26 · arxiv updated 2017/01/27
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.