Quantitative Methods in Classical Perturbation Theory

  • Antonio Giorgilli
Part of the NATO ASI Series book series (NSSB, volume 336)


At the beginning of the second volume of his Méthodes nouvelles de la Mécanique Céleste Poincaré devoted the chapter VIII to the problem of the reliability of the formal expansions of perturbation theory. He proved that the series commonly used in Celestial mechanics are typically non convergent, although their usefulness is generally evident. In particular, he pointed out that these series could have the same character of the Stirling’s series. Recent work in perturbation theory has enlighten this conjecture of Poincaré, bringing into evidence that the series of perturbation theory, although non convergent in general, furnish nevertheless valuable approximations to the true orbits for a very large time, which in some practical cases could be comparable with the age of the universe.


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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Antonio Giorgilli
    • 1
  1. 1.Dipartimento di Matematica dell’Università di MilanoMilanoItaly

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