Work

Periodic points of rational area-preserving homeomorphisms

Year: 2025

Type: article

Abstract: An area-preserving homeomorphism isotopic to the identity is said to have rational rotation direction if its rotation vector is a real multiple of a rational class. We give a short proof that any area-preserving homeomorphism of a compact surface of genus at least two, which is isotopic to the identity and has rational rotation direction, is either the identity or has periodic points of unbounded minimal period. This answers a question of Ginzburg and Seyfaddini and can be regarded as a Conley conjecture-type result for symplectic homeomorphisms of surfaces beyond the Hamiltonian case. We also discuss several variations, such as maps preserving arbitrary Borel probability measures with full support, maps that are not isotopic to the identity and maps on lower genus surfaces. The proofs of the main results combine topological arguments with periodic Floer homology.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2025.10

Author: ROHIL PRASAD

Institution: University of California, Berkeley

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: National Science Foundation, Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley, National Science Foundation Graduate Research Fellowship Program