The stability of subharmonic solutions for Hamiltonian systems
type: Item
instance of: scholarly article
title: The stability of subharmonic solutions for Hamiltonian systems
zbMATH Open document ID: 0951.37003
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-01-02T00:00:00Z
review text: The paper is devoted to the stability of subharmonic solutions of non-autonomous Hamiltonian systems. Under some natural conditions on the Hamiltonian, using the dual Morse index theory, the author obtains an (infinite) sequence of geometrically distinct periodic solutions. Peculiarities of these solutions are: Every element has at most one direction of instability, which in turn implies that at least \(2n-2\) Floquet multipliers are lying on the unit circle in the complex plane if the periodic solution is nondegenerate or all its \(2n\) Floquet multipliers are lying on the unit circle if the periodic solution is degenerate.
Mathematics Subject Classification ID: 37B55
Mathematics Subject Classification ID: 37J05
zbMATH DE Number: 1417578
zbMATH Keywords: non-autonomous Hamiltonian
zbMATH Keywords: subharmonic solutions
zbMATH Keywords: Floquet multipliers
author: Chungen Liu
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6605
OpenAlex ID: W1963876164
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DOI: 10.1006/JMAA.1999.6605
description: scientific article; zbMATH DE number 1417578