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arXiv · 1410.3662

Irrational rotation factors for conservative torus homeomorphisms

T. Jäger·F. A. Tal
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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 $R_α$ 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.

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T. Jäger, F. A. Tal. 2015-09-08. Irrational rotation factors for conservative torus homeomorphisms. https://arxiv.org/abs/1410.3662

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