Bifurcations of symmetric periodic orbits via Floer homology

2019/09/11 by Joontae Kim, Kim, Joontae, Seongchan Kim +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1909.05351

openalex publication_date 2019/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct circular orbits in the rotating Kepler problem and observe bifurcations of torus-type orbits. Our setup is motivated by numerical work of Hénon on Hill's lunar problem.

Citations

• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations

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