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Monotonicity of maximal equicontinuous factors and an application to toral flows

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arxiv 1711.05672 v1 pith:P4DAQUDO submitted 2017-11-15 math.DS

Till Hauser , Tobias Jäger This is my paper · ORCID
classification math.DS
keywords maximalapplicationconnectedequicontinuousfactorirrationaltwo-torusactions
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We show that for group actions on locally connected spaces the maximal equicontinuous factor map is always monotone, that is, the preimages of single points are connected. As an application, we obtain that if the maximal continuous factor of a homeomorphism of the two-torus is minimal, then it is either (i) an irrational translation of the two-torus, (ii) an irrational rotation on the circle or (iii) the identity on a singleton.

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  1. Periodic point free homeomorphisms and irrational rotation factors

    math.DS 2019-08 accept novelty 8.0 of 10

    A non-annular torus homeomorphism with small wandering domains admits an irrational circle factor exactly when it has uniformly bounded rotational deviations in some rational direction.

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