Auslander-Yorke dichotomy theorem, multi-sensitivity and Lyapunov numbers
Dynamical Systems
2016-05-23 v2
Abstract
In this paper we study several stronger forms of sensitivity for continuous surjective selfmaps on compact metric spaces and relations between them. The main result of the paper states that a minimal system is either multi-sensitive or an almost one-to-one extension of its maximal equicontinuous factor, which is an analog of the Auslander-Yorke dichotomy theorem. For minimal dynamical systems, we also show that all notions of thick sensitivity, multi-sensitivity and thickly syndetical sensitivity are equivalent, and all of them are much stronger than sensitivity.
Keywords
Cite
@article{arxiv.1504.00587,
title = {Auslander-Yorke dichotomy theorem, multi-sensitivity and Lyapunov numbers},
author = {Wen Huang and Sergii Kolyada and Guohua Zhang},
journal= {arXiv preprint arXiv:1504.00587},
year = {2016}
}
Comments
The main results of this paper were included in the files arXiv:1509.08813 and arXiv:1509.08818