Periodic Points of Hamiltonian Diffeomorphisms Equal to Nondegenerate Linear Maps at Infinity

2025/10/31 by Li, Meng
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.27193

Abstract

We study Hamiltonian diffeomorphisms on symplectic Euclidean spaces that are equal to non-degenerate linear maps at infinity. Under the assumption that there exists an isolated homologically nontrivial fixed point satisfying the twist condition, we prove the existence of infinitely many simple periodic points. More precisely, if such a diffeomorphism has only finitely many fixed points, then it admits simple periodic points with arbitrarily large prime periods.

Citations

• A Poincaré-Birkhoff Theorem for Asymptotically Unitary Hamiltonian Diffeomorphisms
• Planar Hamiltonian systems: index theory and applications to the existence of subharmonics
• The Conley-Zehnder index for a path of symplectic matrices
• Local Floer Homology and the Action Gap
• The Conley Conjecture
• Coisotropic Intersections
• The Difference Between Consecutive Primes, II
• Propagation in Hamiltonian dynamics and relative symplectic homology
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations

Related

• A Poincaré-Birkhoff Theorem for Asymptotically Unitary Hamiltonian Diffeomorphisms
• On primes and period growth for Hamiltonian diffeomorphisms
• The number of periodic points of surface symplectic diffeomorphisms
• On non-contractible hyperbolic periodic orbits and periodic points of symplectomorphisms
• The Conley Conjecture