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arXiv · 1408.5193

Existence of noncontractible periodic orbits of Hamiltonian system separating two Lagrangian tori on $T^*\T^n$ with application to non convex Hamiltonian systems

Jinxin Xue
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Abstract

In this paper, we show the existence of non contractible periodic orbits in Hamiltonian systems defined on $T^*\T^n$ separating two Lagrangian tori under certain cone assumption. Our result answers a question of Polterovich in \cite{P} in a sharp way. As an application, we find periodic orbits of almost all the homotopy types on a dense set of energy level in Lorentzian type mechanical Hamiltonian systems defined on $T^*\T^2$. This solves a problem of Arnold in \cite{A}.

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Jinxin Xue. 2014-08-22. Existence of noncontractible periodic orbits of Hamiltonian system separating two Lagrangian tori on $T^*\T^n$ with application to non convex Hamiltonian systems. https://arxiv.org/abs/1408.5193

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