Laypunov Irregular Points With Distributional Chaos
Dynamical Systems
2019-07-23 v1
Abstract
It follows from Oseledec Multiplicative Ergodic Theorem (or Kingmans Subadditional Ergodic Theorem) that the Lyapunov-irregular set of points for which the Oseledec averages of a given continuous cocycle diverge has zero measure with respect to any invariant probability measure. In strong contrast, for any dynamical system f with exponential specification property and a Holder continuous matrix cocycle A, we show here that if there exist ergodic measures with different Lyapunov spectrum, then the Lyapunov-irregular set of A displays distributional chaos of type 1.
Cite
@article{arxiv.1907.09400,
title = {Laypunov Irregular Points With Distributional Chaos},
author = {An Chen and Xueting Tian},
journal= {arXiv preprint arXiv:1907.09400},
year = {2019}
}
Comments
13pages. arXiv admin note: text overlap with arXiv:1505.04477, arXiv:1505.04345; text overlap with arXiv:0808.0350 by other authors