On curvature and hyperbolicity of monotone Hamiltonian systems

Paul W. Y. Lee

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arXiv · 1202.3836

On curvature and hyperbolicity of monotone Hamiltonian systems

Paul W. Y. Lee

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Abstract

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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Paul W. Y. Lee. 2012-02-17. On curvature and hyperbolicity of monotone Hamiltonian systems. https://arxiv.org/abs/1202.3836

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