Spatial evaluation of Lyapunov exponents in Hamiltonian systems Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/qb98mh65g

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  • A new method for evaluating the Lyapunov exponent for a Hamiltonian system involves a spatial evaluation, rather than a numerical time integration. The introduction of a novel vector field to the phase space allows the Lyapunov exponent to be expressed in a form that does not involve time. The Lyapunov exponent is seen to be a property of the geometry and topology of ergodic regions of phase space. As a result it has a more regular behavior than previously thought. The Lyapunov exponent is found to be a differentiable function of the perturbation coupling in regions where it was previously thought to be discontinuous. Properties of the Lyapunov function once taken for granted are shown to be artifacts of the traditional computation methods. The technique is discussed with examples from a system of coupled quartic oscillators.
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2012-10-22T22:24:53Z (GMT) No. of bitstreams: 1 StanleyPaulElliott1996.pdf: 2830379 bytes, checksum: e5dad7355ee0a66ae0de50bd3bf11ca2 (MD5)

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