Hamiltonian systems of negative curvature are hyperbolic

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The {\it curvature} and the {\it reduced curvature} are basic differential invariants of the pair: (Hamiltonian system, Lagrange distribution) on the symplectic manifold. We show that negativity of the curvature implies that any bounded semi-trajectory of the Hamiltonian system tends to a hyperbolic equilibrium, while negativity of the reduced curvature implies the hyperbolicity of any compact invariant set of the Hamiltonian flow restricted to a prescribed energy level. Last statement generalizes a well-known property of the geodesic flows of Riemannian manifolds with negative sectional curvatures.
5 pages

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Dynamical Systems, Symplectic Geometry, 37D05; 37D40

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http://salesiana.dossiersoluciones.com/handle/123456789/73176

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411224
 http://arxiv.org/abs/math/0411224

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arXiv