The curvature and hyperbolicity of Hamiltonian systems

  • A. A. Agrachev
Article

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.

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Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • A. A. Agrachev
    • 1
    • 2
  1. 1.SISSA/ISASTriesteItaly
  2. 2.Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

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