Perturbations in a champagne bottle

TitlePerturbations in a champagne bottle
Publication TypeJournal Article
Year of Publication1997
AuthorsGeorgiev G
JournalAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Volume89
IssueLivre 1 - Mathématiques et Mecanique
Pagination141-157
ISSN0205-0808
KeywordsAbelian Integrals, Isoenergetical non-degeneracy, KAM-theory, Kolmogorov's condition
Abstract

The system describing the motion of a particle in a potential field shaped like the bottom of a champagne bottle (more precisely, an $S^{1}$ symmetric double well) for KAM-theory conditions is studied. We show that the Kolmogorov's condition is fulfilled everywhere out of the bifurcation diagram of the energy-momentum map and we make researches for the condition of isoenergetical non-degeneracy.

1991/95 MSC

34D10, 58F07, 58F30, 70H05

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