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The Franks-Misiurewicz conjecture for extensions of irrational rotations

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arxiv 1611.05498 v1 pith:OCWLENPV submitted 2016-11-16 math.DS

classification math.DS
keywords conjecturefranks-misiurewiczirrationalrotationallowsalwayscasecircle
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We show that a toral homeomorphism which is homotopic to the identity and topologically semiconjugate to an irrational rotation of the circle is always a pseudo-rotation (i.e. its rotation set is a single point). In combination with recent results, this allows us to complete the study of the Franks-Misiurewicz conjecture in the minimal case.

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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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