Lyapunov exponents for random perturbations of some area-preserving maps including the standard map
Lyapunov exponents for random perturbations of some area-preserving maps including the standard map
复制标题
DOI：
10.4007/annals.2017.185.1.5
复制
发表时间：
2017-01-01
影响因子：
4.9
通讯作者：
Young, Lai-Sang
中科院分区：
文献类型：
--
作者：
Blumenthal, Alex;Xue, Jinxin;Young, Lai-Sang
我们考虑了一个大类的2D面积保持非均匀双曲，但有很强的双曲性质的相空间的大区域上的仿射。一个典型的例子是标准地图。由于稳定和不稳定方向的潜在切换，这类系统的李雅普诺夫指数的下界很难估计。本文表明，加上（非常）小的随机扰动，一个得到相对容易的Lyapunov指数反映的几何形状的确定性映射。
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.