矩阵上循环的Lyapunov“非典型”点与拓扑熵
动力系统
2015-05-19 v1
摘要
由Oseledec乘法遍历定理（或Kingman的次加性遍历定理）可知，对于给定连续上循环，其Oseledec平均发散的“非典型”点集关于任何不变概率测度具有零测度。形成强烈对比的是，对于双曲系统上的任意Hder连续上循环，本文我们证明要么所有遍历测度具有相同的最大Lyapunov指数，要么Lyapunov“非典型”点集具有满拓扑熵和填充拓扑熵。此外，我们给出了Bowen Hausdorff熵从下方的估计。
引用
@article{arxiv.1505.04345,
title = {Lyapunov `Non-typical' Points of Matrix Cocycles and Topological Entropy},
author = {Xueting Tian},
journal= {arXiv preprint arXiv:1505.04345},
year = {2015}
}
备注
23 pages. arXiv admin note: substantial text overlap with arXiv:0808.0350 by other authors; text overlap with arXiv:0905.0739 by other authors