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

• 成果类型: Article
• 署名作者: Blumenthal, Alex; Xue, Jinxin; Young, Lai-Sang
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.185.1.5
• 发表日期: 2017
• 页码: 285-310
• 关键词: random matrix products; deterministic products; genericity; attractors; families; THEOREM

摘要

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.