Hamiltonian systems of negative curvature are hyperbolic

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dc.creatorAgrachev, Andrei A.
dc.creatorChtcherbakova, Natalia N.
dc.date2004-11-10
dc.date.accessioned2026-07-07T05:14:10Z
dc.date.available2026-07-07T05:14:10Z
dc.descriptionThe {\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.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/math/0411224
dc.identifierhttp://arxiv.org/abs/math/0411224
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73176
dc.subjectDynamical Systems
dc.subjectSymplectic Geometry
dc.subject37D05; 37D40
dc.titleHamiltonian systems of negative curvature are hyperbolic
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