On the geometry of Hamiltonian chaos

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dc.creatorHorwitz, Lawrence
dc.creatorLevitan, Jacob
dc.creatorLewkowicz, Meir
dc.creatorSchiffer, Marcelo
dc.creatorZion, Yossi Ben
dc.date2007-01-18
dc.date2007-04-17
dc.date.accessioned2026-07-07T10:38:45Z
dc.date.available2026-07-07T10:38:45Z
dc.descriptionWe show that Gutzwiller's characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian can be 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 the dual manifold, and the geodesics in the dual space coincide with the orbits of the Hamiltonian potential model. We therefore find a direct geometrical description of the time development of a Hamiltonian potential model. The second covariant derivative of the geodesic deviation in this dual manifold generates a dynamical curvature, resulting in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions giving, in particular, detailed results for a potential obtained from a fifth order expansion of a Toda lattice Hamiltonian.
dc.description7 pages TeX, Figure captions, 4 figures (eps). Some clarifications, added references
dc.identifierhttps://arxiv.org/abs/physics/0701212
dc.identifierhttp://arxiv.org/abs/physics/0701212
dc.identifierPhys.Rev.Lett.98:234301,2007
dc.identifierdoi:10.1103/PhysRevLett.98.234301
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/180834
dc.subjectClassical Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectChaotic Dynamics
dc.subjectGeneral Physics
dc.titleOn the geometry of Hamiltonian chaos
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