A quasiperiodically forced skew-product on the cylinder without fixed-curves
Dynamical Systems
2016-05-31 v1
Abstract
In [FJJK] the Sharkovski\u{i} Theorem was extended to periodic orbits of strips of quasiperiodic skew products in the cylinder. In this paper we deal with the following natural question that arises in this setting: Does Sharkovski\u{i} Theorem holds when restricted to curves instead of general strips?mWe answer this question in the negative by constructing a counterexample: We construct a map having a periodic orbit of period 2 of curves (which is, in fact, the upper and lower circles of the cylinder) and without any invariant curve. In particular this shows that there exist quasiperiodic skew products in the cylinder without invariant curves.
Keywords
Cite
@article{arxiv.1605.08987,
title = {A quasiperiodically forced skew-product on the cylinder without fixed-curves},
author = {Lluís Alsedà and Francesc Mañosas and Leopoldo Morales},
journal= {arXiv preprint arXiv:1605.08987},
year = {2016}
}