Minimal sets of non-resonant torus homeomorphisms

Details Minimal sets of non-resonant torus homeomorphisms Minimal sets of non-resonant torus homeomorphisms

2010-02-01

arxiv.org/abs/1002.0364v2

Fund. Math. 211 (2011), 41-76

Mathematics

Dynamical Systems

40 pages, 5 figures. This is a corrected version (see the Erratum in Fund. Math. 213 (2011), 291) of the original published ve

Scientific paper

10.4064/fm211-1-3

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.

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