Action and rotation number of periodic orbits of area-preserving annulus diffeomorphisms

2025/12/02 by Huadi Qu, Qu, Huadi
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2512.02507

openalex publication_date 2025/12/02 · openalex created_date 2025/12/04 · openalex updated_date 2026/07/28

Abstract

We study periodic orbits for area-preserving surface diffeomorphisms, particularly some global properities related to the action function and rotation numbers. We generalize recent works of Machel Hutchings [4], proving the existence of periodic orbits with certain action and rotation values.

Citations

• Spectral invariants for non-compactly supported Hamiltonians on the disc, and an application to the mean action spectrum
• A finite dimensional proof of a result of Hutchings about irrational pseudo-rotations
• Hutchings' inequality for the Calabi invariant revisited with an application to pseudo-rotations
• Mean action of periodic orbits of area-preserving annulus\n diffeomorphisms
• Mean action and the Calabi invariant

Related

• Action and periodic orbits on annulus
• Mean action of periodic orbits of area-preserving annulus\n diffeomorphisms
• Rotation Numbers and Instability Sets
• Area preserving homeomorphisms of surfaces with rational rotational direction
• Generic density of periodic orbits of area-preserving maps on punctured surfaces