Elliptic stars in a chaotic night
Dynamical Systems
2014-02-26 v2
Abstract
We study homeomorphisms of the two-torus, homotopic to the identity, whose rotation set has non-empty interior. For such maps, we give a purely topological characterisation of elliptic islands in a chaotic sea in terms of local rotation subsets. We further show that the chaotic regime defined in this way cannot contain any Lyapunov stable points. In order to demonstrate our results, we introduce a parameter family inspired by an example of Misiurewicz and Ziemian.
Cite
@article{arxiv.1002.2866,
title = {Elliptic stars in a chaotic night},
author = {T. Jaeger},
journal= {arXiv preprint arXiv:1002.2866},
year = {2014}
}
Comments
15 pages, 7 Figures; Revised versions with some minor corrections.