Elliptic stars in a chaotic night

Details Elliptic stars in a chaotic night Elliptic stars in a chaotic night

2010-02-15

arxiv.org/abs/1002.2866v2

Mathematics

Dynamical Systems

15 pages, 7 Figures; Revised versions with some minor corrections.

Scientific paper

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.

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