Geometry of hamiltonian chaos

Lawrence Horwitz, Yossi Ben Zion, Meir Lewkowicz, Marcelo Schiffer, Jacob Levitan

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Abstract

The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model when a transition is made to an associated manifold. We find, in this way, a direct geometrical description of the time development of a Hamiltonian potential model. The second covariant derivative of the geodesic deviation in this associated manifold results in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions.

Original languageEnglish
Article number234301
JournalPhysical Review Letters
Volume98
Issue number23
DOIs
StatePublished - 4 Jun 2007

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