Spiralling invariant manifolds
type: Item
instance of: scholarly article
title: Spiralling invariant manifolds
zbMATH Open document ID: 0634.58016
DOI: 10.1016/0022-0396(87)90031-3
author: Richard Moeckel
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: This paper is concerned with polar coordinate systems on a neighborhood of codimensional 2 submanifolds, and a definition of the concept of a multidimensional spiralling manifold. The author also develops a criterion for when two spirals which spiral in opposite directions must intersect, and then gives a proof that spirals of this type are created when an invariant manifold passes through a neighborhood of a hyperbolic restpoint with complex eigenvalues. When combined with the intersection theory, the results show that spiralling can function as a mechanism for producing intersections of invariant manifolds in high dimensions. Finally, the author exploits this mechanism to prove the existence of infinitely many solutions of the isosceles 3-body problem which experience triple collisions in both forward and backward time.
Mathematics Subject Classification ID: 37D99
zbMATH DE Number: 4032653
zbMATH Keywords: spiralling invariant manifold
zbMATH Keywords: hyperbolic restpoint
zbMATH Keywords: intersection theory
zbMATH Keywords: 3-body problem
reviewed by: Ding Tongren
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90031-3
OpenAlex ID: W2000242557
cites work: Q3946815
cites work: Triple collision in the planar isosceles three body problem
cites work: Orbits of the Three-Body Problem Which Pass Infinitely Close to Triple Collision
cites work: Chaotic dynamics near triple collision
cites work: On Morse-Smale dynamical systems
cites work: On the Structure of Local Homeomorphisms of Euclidean n-Space, II
description: scientific article; zbMATH DE number 4032653