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On the dynamics of minimal homeomorphisms of $\mathbb{T}^2$ which are not pseudo-rotations

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arxiv 1611.03784 v4 pith:NIQ73GIV submitted 2016-11-11 math.DS

Alejandro Kocsard This is my paper · ORCID
classification math.DS
keywords homeomorphismminimalproverotationassumptionboundedconjectureconsequence
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abstract

We prove that any minimal $2$-torus homeomorphism which is isotopic to the identity and whose rotation set is not just a point exhibits uniformly bounded rotational deviations on the perpendicular direction to the rotation set. As a consequence of this, we show that any such homeomorphism is topologically mixing and we prove Franks-Misiurewicz conjecture under the assumption of minimality.

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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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