Recurrence of non-resonant homeomorphisms on the torus

Potrie, Rafael

doi:10.1090/S0002-9939-2012-11249-3

Recurrence of non-resonant homeomorphisms on the torus
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by Rafael Potrie

Proc. Amer. Math. Soc. 140 (2012), 3973-3981

DOI: https://doi.org/10.1090/S0002-9939-2012-11249-3

Published electronically: March 27, 2012

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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 non-wandering set is weakly transitive. We give an example showing that the non-wandering set of such a homeomorphism may not be transitive.

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