2025/02/17 by Erman Çınelı, Cineli, Erman, Sobhan Seyfaddini +3
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 #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2502.11566
openalex publication_date 2025/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the ergodic closing lemma of Mañé, we investigate the C^∞ closing lemma in higher-dimensional Hamiltonian systems, with a focus on the statistical behavior of periodic orbits generated by C^∞-small perturbations. We demonstrate that, under certain Floer-theoretic conditions, invariant or recurrent Lagrangian submanifolds can give rise to periodic orbits whose statistical properties are controllable. For instance, we show that for Hamiltonian systems preserving the zero section in T^*\mathbbTn, C^∞ generically, there exist periodic orbits converging to an invariant measure supported on the zero section.