Irrational rotation factors for conservative torus homeomorphisms

Abstract

We provide an equivalent characterisation for the existence of one-dimensional irrational rotation factors of conservative torus homeomorphisms that are not eventually annular. It states that an area-preserving non-annular torus homeomorphism $f$ is semiconjugate to an irrational rotation $R_{\alpha }$ of the circle if and only if there exists a well-defined speed of rotation in some rational direction on the torus, and the deviations from the constant rotation in this direction are uniformly bounded. By means of a counterexample, we also demonstrate that a similar characterisation does not hold for eventually annular torus homeomorphisms.

Incorporates referee's corrections. To appear in Ergod. Th. & Dynam. Syst

References in corpus (1)

• Linearisation of conservative toral homeomorphisms