The stability of linear periodic Hamiltonian systems on time scales
type: Item
instance of: scholarly article
title: The stability of linear periodic Hamiltonian systems on time scales
zbMATH Open document ID: 1264.34178
published in: Applied Mathematics Letters
publication date: 2013-01-25T00:00:00Z
review text: The author considers the planar Hamiltonian system \[ x^\Delta=\alpha(t)x^\sigma+\beta(t)u,\;\;u^\Delta=-\gamma(t)x^\sigma-\alpha(t)u \] on an arbitrary time scale \(\mathbb{T}\), where \(\alpha,\beta,\gamma:\mathbb{T}\rightarrow\mathbb{R}\) are rd-continuous, \(\sigma:\mathbb{T}\rightarrow\mathbb{T}\) is the forward jump operator, and \(x^\sigma:=x\circ\sigma\). They give a new stability criterion for planar periodic Hamiltonian systems. The results obtained not only unify the related continuous and discrete ones but also provide sharper stability criteria for the discrete case.
reviewed by: Zhenlai Han
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 37J25
zbMATH DE Number: 6130502
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: time scale
zbMATH Keywords: stability
zbMATH Keywords: Floquet multiplier
author: A. Zafer
MaRDI profile type: Publication
full work available at URL: j.aml.2012.09.014
OpenAlex ID: W2083128412
DOI: 10.1016/J.AML.2012.09.014
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description: scientific article; zbMATH DE number 6130502