Abstract
Poincaré maps for Hamiltonian systems with 3 degrees of freedom lead to the study of four dimensional symplectic mappings. As a test for the validity of a synthetic mapping of order 3 using gradient informations, we study the evolution with time of Liapounov Indicators in the case of the four dimensional standard map with chaotic and stable zones. Both Liapounov Indicators show the same behaviour for the real and synthetic mappings. They reveal exploding diffusion phenomena for temporarily confined chaotic orbits. The distribution of the time of explosion fits well with a Poisson law for the real mapping, but not for the synthetic one. However the mean time of explosion is essentially the same in both cases.
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© 1993 Springer Science+Business Media Dordrecht
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Froeschlé, C., Petit, J.M. (1993). On a Temporary Confinement of Chaotic Orbits of four Dimensional Symplectic Mapping: A Test on the Validity of the Synthetic Approach. In: Bois, E., Oberti, P., Henrard, J. (eds) Interactions Between Physics and Dynamics of Solar System Bodies. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1902-3_12
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DOI: https://doi.org/10.1007/978-94-011-1902-3_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4840-8
Online ISBN: 978-94-011-1902-3
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