Quantitative Methods in Classical Perturbation Theory View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1995

AUTHORS

Antonio Giorgilli

ABSTRACT

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. More... »

PAGES

21-37

References to SciGraph publications

  • 1969-03. Canonical transformations depending on a small parameter in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1985-10. Rigorous estimates for the series expansions of Hamiltonian perturbation theory in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1978-04. Formal integrals for an autonomous Hamiltonian system near an equilibrium point in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • Book

    TITLE

    From Newton to Chaos

    ISBN

    978-1-4899-1087-5
    978-1-4899-1085-1

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-1-4899-1085-1_3

    DOI

    http://dx.doi.org/10.1007/978-1-4899-1085-1_3

    DIMENSIONS

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