Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems

2009/08/01 by Chungen Lıu, Liu, Chungen
Engineering · Mathematics · #58F05. 58E05. 34C25. 58F10 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.0908.0029

openalex publication_date 2009/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems. We prove that if the Hamiltonian function H∈ C²(\Bbb R²ⁿ, \Bbb R) is super-quadratic and convex, for every number τ>0, there exists at least one τ-periodic brake orbit (τ,x) with minimal period τ or τ/2 provided H(Nx)=H(x).

Related

• Minimal period problems for brake orbits of nonlinear autonomous reversible semipositive Hamiltonian systems
• Minimal P-symmetric period problem of first-order autonomous Hamiltonian Systems
• Minimal P-symmetric periodic solutions of nonlinear Hamiltonian systems
• The Rabinowitz minimal periodic solution conjecture on partially convex reversible Hamiltonian systems and brake subharmonics
• The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition