Local stable and unstable sets for positive entropy $C^1$ dynamical systems
Dynamical Systems
2018-08-31 v1
Abstract
For any diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy, a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in terms of the measure-theoretic entropy and the maximal Lyapunov exponent. The mainline of our approach to this result is under the settings of topological dynamical systems, which is also applicable to infinite dimensional dynamical systems.
Cite
@article{arxiv.1808.10156,
title = {Local stable and unstable sets for positive entropy $C^1$ dynamical systems},
author = {Shilin Feng and Rui Gao and Wen Huang and Zeng Lian},
journal= {arXiv preprint arXiv:1808.10156},
year = {2018}
}