Rational Polygons as Rotation Sets of Generic Homeomorphisms of the Two-Torus
Dynamical Systems
2014-02-26 v2
Abstract
We prove the existence of an open and dense set D\subset? Homeo0(T2) (set of toral homeomorphisms homotopic to the identity) such that the rotation set of any element in D is a rational polygon. We also extend this result to the set of axiom A dif- feomorphisms in Homeo0(T2). Further we observe the existence of minimal sets whose rotation set is a non-trivial segment, for an open set in Homeo0(T2).
Keywords
Cite
@article{arxiv.1208.2614,
title = {Rational Polygons as Rotation Sets of Generic Homeomorphisms of the Two-Torus},
author = {Alejandro Passeggi},
journal= {arXiv preprint arXiv:1208.2614},
year = {2014}
}