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arXiv · 1208.2614

Rational Polygons as Rotation Sets of Generic Homeomorphisms of the Two-Torus

Alejandro Passeggi
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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).

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Alejandro Passeggi. 2012-08-20. Rational Polygons as Rotation Sets of Generic Homeomorphisms of the Two-Torus. https://doi.org/10.1112/jlms%2Fjdt040

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