A.A. Agrachev, The Curvature and Hyperbolicity of Hamiltonian Systems

Title: The Curvature and Hyperbolicity of Hamiltonian Systems
Authors: A.A. Agrachev
Journal title: Proc. Steklov Inst. Math.
Year: 2007
Volume: 256
Pages: 26-46
Citation:

A. A. Agrachev, “The Curvature and Hyperbolicity of Hamiltonian Systems”, Proceedings of the Steklov Institute of Mathematics, 2007, 256, 26–46

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.