Transitivity and rotation sets with nonempty interior for homeomorphisms of the 2-Torus

Details Transitivity and rotation sets with nonempty interior for homeomorphisms of the 2-Torus Transitivity and rotation sets with nonempty interior for homeomorphisms of the 2-Torus

2010-12-04

arxiv.org/abs/1012.0909v1

Mathematics

Dynamical Systems

Scientific paper

We show that, if $f$ is a homeomorphism of the 2--torus isotopic to the
identity, and its lift $\widetilde f$ is transitive, or even if it is
transitive outside of the lift of the elliptic islands, then $(0,0)$ is in the
interior of the rotation set of $\widetilde f.$ This proves a particular case
of Boyland's conjecture.

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