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Recurrence of non-resonant homeomorphisms on the torus

By Rafael Potrie

Abstract

We prove that a homeomorphism of the torus homotopic to the identity whose rotation set is reduced to a single totally irrational vector is chain-recurrent. In fact, we show that pseudo-orbits can be chosen with a small number of jumps, in particular, that the nonwandering set is weakly transitive. We give an example showing that the nonwandering set of such a homeomorphism may not be transitive.Comment: 11 pages. Some corrections mad

Topics: Mathematics - Dynamical Systems, 37E45 37B20
Year: 2011
OAI identifier: oai:arXiv.org:1103.4576
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