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On curvature and hyperbolicity of monotone Hamiltonian systems

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 نشر من قبل Paul Woon Yin Lee
 تاريخ النشر 2012
  مجال البحث
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 تأليف Paul W.Y. Lee




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Assume that a Hamiltonian system is monotone. In this paper, we give several characterizations on when such a system is Anosov. Assuming that a monotone Hamiltonian system has no conjugate point, we show that there are two distributions which are invariant under the Hamiltonian flow. We show that a monotone Hamiltonian flow without conjugate point is Anosov if and only if these distributions are transversal. We also show that if the reduced curvature of the Hamiltonian system is non-positive, then the flow is Anosov if and only if the reduced curvature is negative somewhere along each trajectory.



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