On the problem of stability for near to integrable Hamiltonian systems
type: Item
instance of: scholarly article
title: On the problem of stability for near to integrable Hamiltonian systems
zbMATH Open document ID: 0910.58024
author: Antonio Giorgilli
published in: Documenta Mathematica
publication date: 1998-08-05T00:00:00Z
full work available at URL: https://eudml.org/doc/224618
full work available at URL: Giorgilli.MAN.html
review text: The author observes some progress in Nekhoroshev's exponential stability theory made during the last decade, in particular, in the following points. (a) The actual estimates for critical values of small parameters \(\varepsilon\) in singular perturbed Hamiltonian systems for real physical problems; this is illustrated by the stability of Lagrangian point in three bodies problem for Sun-Jupiter case. (b) The extension of the concept of exponential stability with very large number of degrees of freedom and possibly to infinite systems; here a certain one-dimensional model of the gas is under consideration and the author discusses how far the suggestions of Boltzmann and Jeans may be dynamically justified. (c) Some relations between KAM and Nekhoroshev's theories; in particular, a certain stability result is obtained, called superexponential stability.
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 1184354
zbMATH Keywords: perturbation theory
zbMATH Keywords: Nekhoroshev's theory
zbMATH Keywords: exponential stability
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1184354