Stable sets and mean Li–Yorke chaos in positive entropy systems

By Wen Huang, Jian Li, Xiangdong Ye. 2012

59 citations recorded by the source corpus.

Abstract It is shown that in a topological dynamical system with positive entropy, there is a measure-theoretically “rather big” set such that a multivariant version of mean Li–Yorke chaos happens on the closure of the stable or unstable set of any point from the set. It is also proved that the intersections of the sets of asymptotic tuples and mean Li–Yorke tuples with the set of topological entropy tuples are dense in the set of topological entropy tuples respectively.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8972ee2c6da5a8cdf07ed1006a542b0e8d0058c9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Jian Li
2. Xiangdong Ye
3. Wen Huang
4. Felipe Garc'ia-Ramos
5. Guohua Zhang
6. Eli Glasner
7. Hanfeng Li
8. A. Dooley

In Statistical and Nonlinear Physics

1. Jian Li
2. Xiangdong Ye
3. Felipe Garc'ia-Ramos
4. Wen Huang

Citations in the corpus

• Recent development of chaos theory in topological dynamics (2015, background): “9 ([40]) If a dynamical system (X,T ) has positive topological entropy, then there exists a Mycielski multivariant mean Li–Yorke (δn)-scrambled subset K of X, that is, for every n ≥ 2 and every n pairwise distinct points x1, .”