Rotation set of torus homeomorphisms preserving minimal foliations

Abstract

Let f be a homeomorphism on 2-torus, homotopic to the identity and preserving two transverse foliations. If both foliations are minimal, or one is minimal and f has the skew-product form, then f is conjugate to a translation. In particular, the rotation set of f consists of a single point.

Keywords:

• rotation vector
• torus homeomorphism
• minimal foliation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Shaobo Gan is supported by 973 project [grant number 2011CB808002] and NSFC [grant number 11025101], [grant number 11231001]. Yi Shi is supported by China Scholarship Council [grant number 2011601086] and Projeto 090/2013 - PVE/CAPES/CSF.