Inexistence of sublinear diffusion for a class of torus homeomorphisms

Abstract

We prove that, if $f$ is a homeomorphism of the two torus isotopic to the identity whose rotation set is a non-degenerate segment and $f$ has a periodic point, then it has uniformly bounded deviations in the direction perpendicular to the segment.

References in corpus (1)

• Uniform bounds for diffeomorphisms of the torus and a conjecture of P. Boyland