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On the Disappearance of Isolating Integrals in Dynamical Systems with More than Two Degrees of Freedom

Published online by Cambridge University Press:  14 August 2015

C. Froeschlé  and
J.-P. Scheidecker
C. Froeschlé
Affiliation:
Observatoire de Nice, 06300 Nice, France
J.-P. Scheidecker
Affiliation:
Observatoire de Nice, 06300 Nice, France

Abstract

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We continue to study the number of isolating integrals in dynamical systems with three and four degrees of freedom, using as models the measure preserving mappings T already introduced in previous papers (Froeschlé, 1972; Froeschlé and Scheidecker, 1973a).

Thus, we use here a new numerical method which enables us to take as indicator of stochasticity the variation with n of the two (respectively three) largest eigenvalues - in absolute magnitude - of the linear tangential mapping Tn∗ of Tn. This variation appears to be a very good tool for studying the diffusion process which occurs during the disappearance of the isolating integrals, already shown in a previous paper (Froeschlé, 1971). In the case of systems with three degrees of freedom, we define and give an estimation of the diffusion time, and show that the gambler's ruin model is an approximation of this diffusion process.

Type
Research Article
Information
Symposium - International Astronomical Union , Volume 62: The Stability of the Solar System , 1974 , pp. 297 - 310
Copyright
Copyright © Reidel 1974 

References

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