Recurrence of non-resonant homeomorphisms on the torus

Details Recurrence of non-resonant homeomorphisms on the torus Recurrence of non-resonant homeomorphisms on the torus

2011-03-23

arxiv.org/abs/1103.4576v2

Mathematics

Dynamical Systems

11 pages. Some corrections made

Scientific paper

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.

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