Frequency analysis of a dynamical system
type: Item
instance of: scholarly article
title: Frequency analysis of a dynamical system
zbMATH Open document ID: 0785.58025
DOI: 10.1007/BF00699731
author: Jacques Laskar
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1994-04-27T00:00:00Z
review text: Frequency analysis method was devised to study stability of motions in the solar system and was proved to be a powerful method for analyzing the stability of orbits in a conservative dynamical system, particularly, weakly chaotic motions in Hamiltonian systems or symplectic maps. For regular motion it yields an analytical representation of the solutions. In this paper the author shows precise numerical criteria for the destruction of KAM tori for the case of dynamical systems of two degrees of freedom with monotonous torsion. It is also shown that for a 4D symplectic map plotting the frequency map in the frequency plane provides a clear representation of the global dynamics and describes the actual Arnold web of the system.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 86A17
zbMATH DE Number: 429321
zbMATH Keywords: frequency analysis
zbMATH Keywords: chaotic motions
zbMATH Keywords: symplectic maps
reviewed by: Yoshihide Kozai
MaRDI profile type: Publication
cites work: Q5640778
cites work: The measure of chaos by the numerical analysis of the fundamental frequencies. Applications to the standard mapping
cites work: Integrability of hamiltonian systems on cantor sets
full work available at URL: https://doi.org/10.1007/bf00699731
OpenAlex ID: W4240145381
description: scientific article; zbMATH DE number 429321