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October  2016, 36(10): 5257-5266. doi: 10.3934/dcds.2016030

## Restrictions on rotation sets for commuting torus homeomorphisms

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

Received  October 2015 Revised  February 2016 Published  July 2016

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.
Citation: Deissy M. S. Castelblanco. Restrictions on rotation sets for commuting torus homeomorphisms. Discrete & Continuous Dynamical Systems, 2016, 36 (10) : 5257-5266. doi: 10.3934/dcds.2016030
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