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

@article{Blumenthal2017LyapunovEF,
title={Lyapunov exponents for random perturbations of some area-preserving maps including the standard map},
author={Alex Blumenthal and Jinxin Xue and Lai-Sang Young},
journal={Annals of Mathematics},
year={2017},
volume={185},
pages={285-310}
}
• Published 26 January 2017
• Mathematics
• Annals of Mathematics
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…
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