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On curvature and hyperbolicity of monotone Hamiltonian systems
- Publication Year :
- 2012
-
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.<br />Comment: 34 pages, some typos are fixed in the new version
- Subjects :
- Mathematics - Dynamical Systems
37D20
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1202.3836
- Document Type :
- Working Paper