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February  2010, 27(1): 337-355. doi: 10.3934/dcds.2010.27.337

Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems

Chungen Liu 1,

1. 

School of Mathematics and LPMC, Nankai University, Tianjin 300071, China

Received  March 2009 Revised  November 2009 Published  February 2010

In this paper, we consider the minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems. We prove that if the Hamiltonian function $H\in C^2(\R^{2n}, \R)$ is super-quadratic and convex, for every number $\tau>0$, there exists at least one $\tau$-periodic brake orbit $(\tau,x)$ with minimal period $\tau$ or $\tau/2$ provided $H(Nx)=H(x)$.
Keywords: Hamiltonian systems, minimal period problem., index iteration theory.
Mathematics Subject Classification: Primary: 58F05, 58E05; Secondary: 34C25, 58F1.
Citation: Chungen Liu. Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 337-355. doi: 10.3934/dcds.2010.27.337
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