Quantitative perturbation theory by successive elimination of harmonics
type: Item
instance of: scholarly article
title: Quantitative perturbation theory by successive elimination of harmonics
zbMATH Open document ID: 0772.58049
DOI: 10.1007/BF00692425
author: Alessandro Morbidelli
author: Antonio Giorgilli
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1993-05-16T00:00:00Z
review text: This paper establishes the theoretical basis for the method presented by the first author [see the previous review, ibid., 101-130 (1993)]. Two theorems are proved. The first one proves the ``almost invariantness within the limit \(T\) in time'' of tori constructed by the method. These tori fill up in the phase space an open set \(A\), say. The second theorem presents an estimate for \(T\) of exponential type that guarantees that the set \(A\) contains open balls of a given radius.
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 70F15
zbMATH DE Number: 167662
zbMATH Keywords: perturbation
zbMATH Keywords: KAM theorem
zbMATH Keywords: Nekhoroshev theorem
zbMATH Keywords: action-angle variables
reviewed by: Yu. N. Bibikov
MaRDI profile type: Publication
cites work: SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
cites work: On the stability of the Lagrangian points in the spatial restricted problem of three bodies
cites work: Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
cites work: A semi-numerical perturbation method for separable Hamiltonian systems
cites work: Complex analysis and convolution operators
cites work: On the successive elimination of perturbation harmonics
cites work: AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
description: scientific article; zbMATH DE number 167662