Geodesic
Minimal sets of non-resonant torus homeomorphisms
Ferry Kwakkel1
1 Mathematics Institute University of Warwick CV4 7AL, Coventry, United Kingdom
Fundamenta Mathematicae, Tome 211 (2011) no. 1, pp. 41-76.

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As was known to H. Poincaré, 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.
DOI : 10.4064/fm211-1-3
Keywords: known poincar orientation preserving circle homeomorphism without periodic points either minimal has dense orbits every orbit accumulates unique minimal set first minimal set circle latter cantor set paper study two dimensional analogue classical result classify minimal sets non resonant torus homeomorphisms torus homeomorphisms isotopic identity which rotation set point rationally independent irrational coordinates

Ferry Kwakkel 1

1 Mathematics Institute University of Warwick CV4 7AL, Coventry, United Kingdom 
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Ferry Kwakkel. Minimal sets of non-resonant torus homeomorphisms. Fundamenta Mathematicae, Tome 211 (2011) no. 1, pp. 41-76. doi : 10.4064/fm211-1-3. http://geodesic.mathdoc.fr/articles/10.4064/fm211-1-3/

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