An improved estimate for the maximal growth order of solutions of linear differential systems
type: Item
instance of: scholarly article
title: An improved estimate for the maximal growth order of solutions of linear differential systems
zbMATH Open document ID: 1054.34058
author: Eckhard Pflügel
published in: Archiv der Mathematik
publication date: 2004-11-05T00:00:00Z
review text: Consider a linear system of ordinary differential equations \(x^{r+1}\frac {dy}{dx}=Ay\), where \(y\) is a vector with \(n\geq2\) components, \(r\) a positive integer, called the Poincaré-rank of the system, and \(A\) a square formal power series matrix of dimension \(n\) of the form \(A=\sum_{\nu=0}^{\infty}A_{\nu }x^{\nu}\), \(A_{0}\neq0\), where the \(A_{\nu}\) are constant matrices with entries in \(\mathbb C\). Let also \(A_{0}\) be a nilpotent matrix and the system is not reducible as defined by \textit{J. Moser} [Math. Z. 72, 379--398 (1960; Zbl 0117.04902)]. The paper improves the estimate on the maximal growth order \(\rho\) of a fundamental solution of the system. This result can be useful when designing algorithms for \(\rho\) and related other invariants.
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 2113844
zbMATH Keywords: maximal growth order
zbMATH Keywords: reducible
zbMATH Keywords: strict equivalence
zbMATH Keywords: linear differential systems
reviewed by: Nicholas Karampetakis
MaRDI profile type: Publication
full work available at URL: s00013-004-1058-3
OpenAlex ID: W2165343208
DOI: 10.1007/S00013-004-1058-3
description: scientific article; zbMATH DE number 2113844