Imbeddings of integral submanifolds and associated adiabatic invariants of slowly perturbed integrable Hamiltonian systems

Document Type

Article

Publication Date

1-1-1999

Abstract

A new method is developed for characterizing the evolution of invariant tori of slowly varying perturbations of completely integrable (in the sense of Liouville-Arnold [1-3]) Hamiltonian systems on cotangent phase spaces. The method is based on Cartan's theory of integral submanifolds, and it provides an algebro-analytic approach to the investigation of the embedding [4-10] of the invariant tori in phase space that can be used to describe the structure of quasi-periodic solutions on the tori. In addition, it leads to an adiabatic perturbation theory [3,12,13] of the corresponding Lagrangian asymptotic submanifolds via the Poincaré-Cartan approach [4], a new Poincaré-Melnikov type [5,11,14] procedure for determining stability, and fresh insights into the existence problem for adiabatic invariants [2,3] of the Hamiltonian systems under consideration.

Identifier

0033177766 (Scopus)

Publication Title

Reports on Mathematical Physics

External Full Text Location

https://doi.org/10.1016/s0034-4877(99)80158-x

ISSN

00344877

First Page

171

Last Page

182

Issue

1-2

Volume

44

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