On curvature and hyperbolicity of monotone Hamiltonian systems
Dynamical Systems
2012-07-31 v3
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.
Keywords
Cite
@article{arxiv.1202.3836,
title = {On curvature and hyperbolicity of monotone Hamiltonian systems},
author = {Paul W. Y. Lee},
journal= {arXiv preprint arXiv:1202.3836},
year = {2012}
}
Comments
34 pages, some typos are fixed in the new version