Minimal P-symmetric period problem of first-order autonomous Hamiltonian Systems

2016/12/13 by Chungen Lıu, Liu, Chungen, Ben-Xing Zhou +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1612.04033

openalex publication_date 2016/12/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Let P∈ Sp(2n) satisfying P^k=I_2n, we consider the minimal P-symmetric period problem of the autonomous nonlinear Hamiltonian system x(t) = JH^′(x(t)). For some symplectic matrices P, we show that for any τ>0 the above Hamiltonian system possesses a kτ periodic solution x with kτ being its minimal P-symmetric period provided H satisfies the Rabinowitz's conditions on the minimal period conjecture, together with that H is convex and H(Px)=H(x).

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