Multiple Rotation Type Solutions for Hamiltonian Systems on T^ℓ×ℝ^2n-ℓ

2010/03/21 by Hui Qiao, Qiao, Hui
Mathematics · Physics and Astronomy · #37J45 #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Symplectic Geometry (math.SG) #math.SG #msc:37J45

paper · pdf · doi:10.48550/arxiv.1003.4035

30 pages, 3 figures

arxiv created 2010/03/21 · openalex publication_date 2010/03/21 · arxiv updated 2010/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with multiplicity of rotation type solutions for Hamiltonian systems on T^ℓ× ℝ^2n-ℓ. It is proved that, for every spatially periodic Hamiltonian system, i.e., the case ℓ=n, there exist at least n+1 geometrically distinct rotation type solutions with given energy rotation vector. It is also proved that, for a class of Hamiltonian systems on T^ℓ×ℝ^2n-ℓ with 1\leqslantℓ\leqslant 2n-1 but ℓ≠ n, there exists at least one periodic solution or n+1 rotation type solutions on every contact energy hypersurface.

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