Restrictions on rotation sets for commuting torus homeomorphisms

Deissy M. S.  Castelblanco

doi:10.3934/dcds.2016030

Article Contents

2016, Volume 36, Issue 10: 5257-5266. Doi: 10.3934/dcds.2016030

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Restrictions on rotation sets for commuting torus homeomorphisms

Deissy M. S. Castelblanco^1,

1.
Rua do Matão 1010, IME-USP, São Paulo, SP

Received: October 2015

Revised: February 2016

Published: May 2017

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Abstract

Let $K_1,\: K_2\subset \mathbb{R}^2$ be two convex, compact sets. We would like to know if there are commuting torus homeomorphisms $f$ and $h$ homotopic to the identity, with lifts $\tilde f$ and $\tilde h$ such that $K_1$ and $K_2$ are their rotation sets respectively. In this work, we prove some cases where it cannot happen, assuming some restrictions on rotation sets.

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Mathematics Subject Classification: Primary: 37E30, 37E45, 37B05.

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References

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