Curvature-type invariants of Hamiltonian systems generalize sectional curvatures of Riemannian manifolds: the negativity of the curvature is an indicator of the hyperbolic behavior of the Hamiltonian flow. In this paper, we give a self-contained description of the related constructions and facts; they lead to a natural extension of the classical results about Riemannian geodesic flows and indicate some new phenomena.
The curvature and hyperbolicity of Hamiltonian systems / Agrachev, Andrey. - In: PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - ISSN 0081-5438. - 256:1(2007), pp. 26-46. [10.1134/S0081543807010026]
The curvature and hyperbolicity of Hamiltonian systems
Agrachev, Andrey
2007-01-01
Abstract
Curvature-type invariants of Hamiltonian systems generalize sectional curvatures of Riemannian manifolds: the negativity of the curvature is an indicator of the hyperbolic behavior of the Hamiltonian flow. In this paper, we give a self-contained description of the related constructions and facts; they lead to a natural extension of the classical results about Riemannian geodesic flows and indicate some new phenomena.File in questo prodotto:
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