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On the Number of Isolating Integrals in Systems with Three Degrees of Freedom

Published online by Cambridge University Press:  12 April 2016

Claude Froeschle
Claude Froeschle*
Affiliation:
Observatoire de Nice, Le Mont-Gros, 06 Nice (France)

Abstract

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Dynamical systems with three degrees of freedom can be reduced to the study of a four-dimensional mapping. We consider here, as a model problem, the mapping given by the following equations:

We have found that as soon as b ≠ 0, i.e. even for a very weak coupling, a dynamical system with three degrees of freedom has in general either two or zero isolating integrals (besides the usual energy integral).

Type
Research Article
Information
International Astronomical Union Colloquium , Volume 10: Gravitational N-Body Problem , November 1971 , pp. 110 - 117
Copyright
Copyright © Reidel 1971

References

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