The measure of chaos by the numerical analysis of the fundamental frequencies. Applications to the standard mapping
type: Item
instance of: scholarly article
title: The measure of chaos by the numerical analysis of the fundamental frequencies. Applications to the standard mapping
zbMATH Open document ID: 0761.58034
DOI: 10.1016/0167-2789(92)90028-L
author: Jacques Laskar
author: Claude Froeschlé
author: Alessandra Celletti
published in: Physica D
publication date: 1993-01-16T00:00:00Z
review text: The first author has developed a new method for the measure of chaos [The chaotic behaviour of the solar system: A numerical estimate of the size of the chaotic zones, Icarus 88, 266-291 (1990)], which is based on the numerical analysis of the variations of fundamental frequencies with time. The method is well suited for the analysis of weakly chaotic motion with many degrees of freedom, and it was first applied for studying the stability of the solar system. As the new method is likely to be of considerable interest for a large range of practical problems, its theoretical foundations with applications to the standard mapping are presented in the paper under review. It is shown that the method allows to obtain an analytical representation of the solution when it is regular, to detect if an orbit is chaotic in a shorter time span as compared with the computation of Lyapunov exponents, and it also gives an estimate of the size of the chaotic zones in the frequency domain.
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 91656
zbMATH Keywords: weakly chaotic motion with many degrees of freedom
MaRDI profile type: Publication
cites work: Invariant curves for area-preserving twist maps far from integrable
cites work: The Lyapunov characteristic exponents-applications to celestial mechanics
cites work: Q4720438
cites work: Inégalités ``a priori'' pour des tores lagrangiens invariants par des difféomorphismes symplectiques. (`A priori' inequalities for Langrangian tori invariant under symplectic diffeomorphisms)
cites work: Converse KAM: theory and practice
cites work: Stability of \(C^ \infty\) mappings. V: Transversality
cites work: An obstruction method for the destruction of invariant curves
full work available at URL: 0167-2789(92)90028-l
OpenAlex ID: W2033167869
description: scientific article; zbMATH DE number 91656