Minimal period estimates for brake orbits of nonlinearsymmetric Hamiltonian systems

Chungen Liu

doi:10.3934/dcds.2010.27.337

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2010, Volume 27, Issue 1: 337-355. Doi: 10.3934/dcds.2010.27.337

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Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems

Chungen Liu^1,

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

Received: February 28, 2009

Revised: October 31, 2009

Published: February 2010

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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 $H\in C^2(\R^{2n}, \R)$ 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 $H(Nx)=H(x)$.

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Mathematics Subject Classification: Primary: 58F05, 58E05; Secondary: 34C25, 58F10.

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