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Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds

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


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