Closed trajectories on symmetric convex Hamiltonian energy surfaces

2009/09/19 by Wei Wang, Wang, Wei · 2 citations
Mathematics · Physics and Astronomy · #37C75. #37J45 #58E05 #FOS: Mathematics #Graph theory and applications #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Symplectic Geometry (math.SG) #math.SG #msc:37C75. #msc:37J45 #msc:58E05

paper · pdf · doi:10.48550/arxiv.0909.3564

27pages

arxiv created 2009/09/19 · openalex publication_date 2009/09/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, let Σ⊂\R²ⁿ be a compact convex Hamiltonian energy surface which is symmetric with respect to the origin. where n≥ 2. We prove that there exist at least two geometrically distinct symmetric closed trajectories of the Reeb vector field on \Sg.

Citations

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

Cited by

• Stable P-symmetric closed characteristics on partially symmetric compact convex hypersurfaces
• Resonance identities and stability of symmetric closed characteristics on symmetric compact star-shaped hypersurfaces

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