Generic Rotation Sets in Hyperbolic Surfaces

2020/06/22 by J. Alonso, Alonso, J., Joaquín Brum +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2006.12345

openalex publication_date 2020/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for generic homeomorphisms homotopic to the identity in a closed and oriented surface of genus g>1, the rotation set is given by a union of at most 2^5g-3 convex sets. Examples showing the sharpness for this asymptotic order are provided.

Related

• Surface homeomorphisms with big rotation set
• Homotopic rotation sets for higher genus surfaces
• A rotational hyperbolic theory for surface homeomorphisms
• Hyperbolic isometries of the fine curve graph of higher genus surfaces
• Every convex polygon with rational vertices is a rotation set