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

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 نشر من قبل Jinxin Xue
 تاريخ النشر 2014
  مجال البحث
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 تأليف Jinxin Xue




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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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