On torus homeomorphisms whose rotation set is an interval

2011/11/10 by Pablo Dávalos, Dávalos, Pablo · 1 citation
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1111.2378

openalex publication_date 2011/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for a torus homeomorphism isotopic to the identity and with a lift whose rotation set is an interval, either every rational point in the rotation set is realized by a periodic orbit, or there exists an annular, essential, periodic set. In the latter case we give a qualitative description of the dynamics.

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