Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems

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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

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

Received March 2009 Revised November 2009 Published February 2010

Abstract
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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 & Continuous Dynamical Systems - A, 2010, 27 (1) : 337-355. doi: 10.3934/dcds.2010.27.337

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