Conditional Entropy |
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| Authors: | P Cincotta C Simó |
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| Institution: | (1) Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque, 1900 La Plata, Argentina;(2) Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain, e-mail |
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| Abstract: | In this paper we show that the Conditional Entropy of nearby orbits may be a useful tool to explore the phase space associated
to a given Hamiltonian. The arc length parameter along the orbits, instead of the time, is used as a random variable to compute
the entropy. In the first part of this work we summarise the main analytical results to support this tool while, in the second
part, we present numerical evidence that this technique is able to localise (stable) periodic and quasiperiodic orbits, 'aperiodic'
orbits (chaotic motion) and unstable periodic orbits (the 'source' of chaotic motion). Besides, we show that this technique
provides a measure of chaos which is similar to that given by the largest Lyapunov Characteristic Number. It is important
to remark that this method is very simple to compute and does not require long time integrations, just realistic physical
times.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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| Keywords: | Chaos Lyapunov Characteristic Number Entropy |
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