A note on the matrix solution of the problem \(X^{\Delta} = AX, X(t_{0}) = I\)
type: Item
instance of: scholarly article
title: A note on the matrix solution of the problem \(X^{\Delta} = AX, X(t_{0}) = I\)
zbMATH Open document ID: 1074.39017
publication date: 2005-06-01T00:00:00Z
review text: Let \({\mathbb T}\) be a time scale, i.e. a nonempty closed subset of \({\mathbb R}\). The author considers special time scales for which the set of certain ``pathological'' points (which are left-dense and right-dense at the same time) has the Lebesgue measure zero. For such time scales, the author derives a representation of the fundamental matrix \(X(t)\) of the linear autonomous dynamic system \(X^\Delta=AX\), where \(A\) is an \(n\times n\) regressive matrix. This is achieved by considering certain (infinite) matrix product with the usual matrix exponential.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 2173420
zbMATH Keywords: time scale
zbMATH Keywords: matrix exponential
zbMATH Keywords: linear autonomous equation
zbMATH Keywords: fundamental matrix
zbMATH Keywords: unification of difference and differential calculus
zbMATH Keywords: dynamic system
author: Ladislav Adamec
reviewed by: Roman Šimon Hilscher
MaRDI profile type: Publication
full work available at URL: j.camwa.2004.07.006
OpenAlex ID: W2025604180
cites work: Q3198160
cites work: Dynamic equations on time scales: A survey
cites work: First and second order linear dynamic equations on time scales
cites work: Floquet Theory for Time Scales and Putzer Representations of Matrix Logarithms
DOI: 10.1016/J.CAMWA.2004.07.006
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2173420