The Liapunov exponent as a tool for exploring phase space
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Data
1996-01-01
Autores
Winter, O. C.
Murray, C. D.
Muzzio, J. C.
FerrazMello, S.
Henrard, J.
Título da Revista
ISSN da Revista
Título de Volume
Editor
Kluwer Academic Publ
Resumo
We have used the Liapunov exponent to explore the phase space of a dynamical system. Considering the planar, circular restricted three-body problem for a mass ratio mu = 10(-3) (close to the Jupiter/Sun case), we have integrated similar to 16,000 starting conditions for orbits started interior to that of the perturber and we have estimated the maximum Liapunov characteristic exponent for each starting condition. Despite the fact that the integrations, in general, are for only a few thousand orbital periods of the secondary, a comparative analysis of the Liapunov exponents for various values of the 'cut-off' gives a good overview of the structure of the phase space. It provides information about the diffusion rates of the various chaotic regions, the location of the regular regions associated with primary resonances and even details such as the location of secondary resonances that produce chaotic regions inside the regular regions of primary resonances.
Descrição
Palavras-chave
chaos, Liapunov exponents, orbits
Como citar
Chaos In Gravitational N-body Systems. Dordrecht: Kluwer Academic Publ, p. 215-219, 1996.