2024/11/23 by Shaoyang Zhou, Zhou, Shaoyang
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2411.15429
openalex publication_date 2024/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the dynamics of area-preserving maps in a non-compact setting. We show that the C∞-closing lemma holds for area-preserving diffeomorphisms on a closed surface with finitely many points removed. As a corollary, a C∞-generic area-preserving diffeomorphism on such a surface has a dense set of periodic points. For area-preserving maps on a finitely punctured 2-sphere, we establish a more quantitative result regarding the equidistribution of periodic orbits. The proof of this result involves a PFH Weyl law for rational area-preserving homeomorphisms, which may be of independent interest.