On torus homeomorphisms whose rotation set is an interval

Abstract

We prove that for a torus homeomorphism isotopic to the identity and with a lift whose rotation set is an interval, either every rational point in the rotation set is realized by a periodic orbit, or there exists an annular, essential, periodic set. In the latter case we give a qualitative description of the dynamics.

50 pages, 17 figures. Addendum B was added. Accepted and corrected version, to appear in Math. Z

References in corpus (1)

• Area-preserving irrotational diffeomorphisms of the torus with sublinear diffusion

Cited by in corpus (2)

• Ergodicity and annular homeomorphisms of the torus
• A characterization of annularity for area-preserving toral homeomorphisms