The existence of homoclinic motions
type: Item
instance of: scholarly article
title: The existence of homoclinic motions
zbMATH Open document ID: 0549.58019
published in: Moscow University Mathematics Bulletin
publication date: 1983-01-01T00:00:00Z
review text: A motion of a Hamiltonian system is said to be homoclinic, or doubly- periodic, if it tends asymptotically to a periodic motion as \(t\to\pm \infty\). The main result of the concisely written paper is presented in the form of the following theorem: Let \(\gamma\) be a minimal periodic motion with non-vanishing characteristic determinants. Then a homoclinic motion to \(\gamma\) exists. Morse theory is employed to prove the theorem. To understand the paper the reader should be acquainted with two previous contributions by the author [Vestn. Mosk. Univ., Ser. I 1978, No.6, 72-77 (1978; Zbl 0403.34053)] and by \textit{V. V. Kozlov} and the author [ibid. 1980, No.4, 84-89 (1980; Zbl 0439.70020)].
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 70H99
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 3876256
zbMATH Keywords: P-S condition
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: periodic motion
zbMATH Keywords: homoclinic motion
zbMATH Keywords: Morse theory
author: S. V. Bolotin
reviewed by: W. Bielski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3876256