On the extendable regular integrals of the n-body problem
type: Item
instance of: scholarly article
title: On the extendable regular integrals of the n-body problem
zbMATH Open document ID: 0563.70009
DOI: 10.1016/0022-0396(84)90159-1
author: Jaume Llibre
published in: Journal of Differential Equations
publication date: 1984-01-01T00:00:00Z
review text: The paper deals with the n-body problem in d-dimensional space. The author calls an integral F ''extendable regular integral'' of the problem, if F is in involution to the classical integrals and if F can be extended to the total collision manifold. The main result is: the n-body problem in a d-dimensional space has no extendable regular integrals if \(n\geq d+1\).
Mathematics Subject Classification ID: 70F10
zbMATH DE Number: 3898287
zbMATH Keywords: n-body problem in d-dimensional space
zbMATH Keywords: extendable regular integral
zbMATH Keywords: total collision manifold
MaRDI profile type: Publication
full work available at URL: 0022-0396(84)90159-1
OpenAlex ID: W2039269174
cites work: Q4174811
cites work: On the integral manifolds of the n-body problem
cites work: Q3674125
cites work: Structural stability of homothetic solutions of the collinearn-body problem
cites work: Q3920693
cites work: Characterization of transversal homothetic solutions in the n-body problem
cites work: Triple collision in the collinear three-body problem
cites work: Classifying relative equilibria. II
cites work: On the role and the properties ofn body central configurations
cites work: Topology and mechanics. II: The planar \(n\)-body problem
cites work: Q5529233
description: scientific article; zbMATH DE number 3898287