Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-27T12:02:01.813Z Has data issue: false hasContentIssue false
  • English
  • Français

On the measure of the structure around an invariant KAM torus

Analytical and Numerical Investigation

Published online by Cambridge University Press:  25 May 2016

C. Froeschlé ,
A. Giorgilli ,
E. Lega  and
A. Morbidelli
C. Froeschlé
Affiliation:
Observatoire de Nice B.P.229, 06304 Nice cedex 4
A. Giorgilli
Affiliation:
Dipartimento di Fisica dell'Università, Via Celoria 16, Milan
E. Lega
Affiliation:
Observatoire de Nice B.P.229, 06304 Nice cedex 4 LATAPSES, 250 Rue A. Einstein, 06560 Valbonne
A. Morbidelli
Affiliation:
Observatoire de Nice B.P.229, 06304 Nice cedex 4

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In a recent paper, Morbidelli and Giorgilli (1995) proved the superexponential stability of invariant tori. As usual in the theory of dynamical systems, the results are rigorously proved assuming that the perturbation is small enough. The numerical experiments show, however, that invariant tori persist up to much larger perturbation magnitudes. Therefore, it is interesting to check numerically if the superexponential stability and the other properties outlined in Morbidelli and Giorgilli's theorem persist up to the value of the perturbation for which the torus actually breaks up. Moreover, one would like to have a numerical indication about the size of the super-exponentially stable region existing around a torus. Is the superexponential stability just an asymptotic result, or does it concern a macroscopic region of physical interest?

Type
Part VII - The Calculus of Perturbations
Information
Symposium - International Astronomical Union , Volume 172: Dynamics, Ephemerides and Astrometry of the Solar System , 1996 , pp. 293 - 298
Copyright
Copyright © Kluwer 1996 

References

Arnold, V. I. (1963), Russ. math. Surv., 18, 9.CrossRefGoogle Scholar
Hénon, M. (1969), Quarterly of Applied Mathematics, 27, 291–306.Google Scholar
Kolmogorov, A. N (1954), Dokl. Akad. Nauk. SSSR, 98, 527 Google Scholar
Laskar, J., Froeschlé, C. and Celletti, A. (1992), Physica D, 56, 253.CrossRefGoogle Scholar
Lega, E. and Froeschlé, C. (1995), submitted to Physica D..Google Scholar
Morbidelli, A. and Giorgilli, A. (1995), J. Stat. Phys., 78, 1607.CrossRefGoogle Scholar
Nekhoroshev, N. N. (1977), Russ. math. Surveys, 32, 1–65.CrossRefGoogle Scholar