Minimal sets of non-resonant torus homeomorphisms
Dynamical Systems
2014-05-06 v3
Abstract
As was known to H. Poincare, an orientation preserving circle homeomorphism without periodic points is either minimal or has no dense orbits, and every orbit accumulates on the unique minimal set. In the first case the minimal set is the circle, in the latter case a Cantor set. In this paper we study a two-dimensional analogue of this classical result: we classify the minimal sets of non-resonant torus homeomorphisms; that is, torus homeomorphisms isotopic to the identity for which the rotation set is a point with rationally independent irrational coordinates.
Keywords
Cite
@article{arxiv.1002.0364,
title = {Minimal sets of non-resonant torus homeomorphisms},
author = {Ferry Kwakkel},
journal= {arXiv preprint arXiv:1002.0364},
year = {2014}
}
Comments
Corrected version of Fund. Math. 211 (2011), pp. 41-76, see erratum in Fund. Math. 213 (2011), p. 291