Generic equidistribution of periodic orbits for area-preserving surface maps

2021/12/29 by Rohil Prasad, Prasad, Rohil · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2112.14601

openalex publication_date 2021/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a C^∞-generic area-preserving diffeomorphism of a closed, oriented surface admits a sequence of equidistributed periodic orbits. This is a quantitative refinement of the recently established generic density theorem for area-preserving surface diffeomorphisms. The proof has two ingredients. The first is a "Weyl law" for PFH spectral invariants, which was used to prove the generic density theorem. The second is a variational argument inspired by the work of Marques-Neves-Song and Irie on equidistribution results for minimal hypersurfaces and three-dimensional Reeb flows, respectively.

Cited by

• Strong closing lemmas in Hamiltonian dynamics

Related

• Generic equidistribution for area-preserving diffeomorphisms of compact surfaces with boundary
• Generic density of periodic orbits of area-preserving maps on punctured surfaces
• Equidistributed periodic orbits of C^∞-generic three-dimensional Reeb flows
• A C^∞ closing lemma on torus
• PFH spectral invariants and C^∞ closing lemmas