Heteroclinic orbits for a class of Hamiltonian systems  onRiemannian manifolds

Fei Liu; Jaume Llibre; Xiang Zhang

doi:10.3934/dcds.2011.29.1097

Article Contents

2011, Volume 29, Issue 3: 1097-1111. Doi: 10.3934/dcds.2011.29.1097

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Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds

1.
Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240
2.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona

Received: February 28, 2009

Revised: August 31, 2010

Published: August 2011

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Abstract

Let $\mathcal M$ be a smooth Riemannian manifold with the metric $(g_{ij})$ of dimension $n$, and let $H= 1/2 g^{ij}(q)p_ip_j+V(t,q)$ be a smooth Hamiltonian on $\mathcal M$, where $(g^{ij})$ is the inverse matrix of $(g_{ij})$. Under suitable assumptions we prove the existence of heteroclinic orbits of the induced Hamiltonian systems.

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Mathematics Subject Classification: Primary: 37C29, 37J45, 70H05; Secondary: 34C37, 37C10.

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