Hamiltonian perturbation theory on a manifold
type: Item
instance of: scholarly article
title: Hamiltonian perturbation theory on a manifold
zbMATH Open document ID: 0840.58039
DOI: 10.1007/BF00692068
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1996-07-07T00:00:00Z
review text: The author develops a ``global'' formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system does not possess a global system of coordinates of action-angle type which is the key for this study. This degenerate system can be described by some generalizations of the Liouville-Arnold's theorem. As an application a ``global'' formulation of Nekhoroshev's theorem on the stability for exponentially long times is given.
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 70H99
zbMATH DE Number: 798823
zbMATH Keywords: bifurcations
zbMATH Keywords: global action-angle coordinates
zbMATH Keywords: Hamiltonian perturbation theory
zbMATH Keywords: degenerate Hamiltonian systems
zbMATH Keywords: Nekhoroshev's theorem
author: Francesco Fassò
reviewed by: G.V.Khmelevskaja-Plotnikova
MaRDI profile type: Publication
cites work: Q4771891
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description: scientific article; zbMATH DE number 798823