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International Journal of Differential Equations
Volume 2013 (2013), Article ID 740980, 11 pages
http://dx.doi.org/10.1155/2013/740980
Research Article

Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations

1Ehime University, Matsuyama 790-8577, Japan
2Department of Mathematics, University of Zagreb, FER, 10000 Zagreb, Croatia

Received 2 April 2013; Accepted 21 May 2013

Academic Editor: Norio Yoshida

Copyright © 2013 Yūki Naito and Mervan Pašić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a new kind of asymptotic behaviour near for the nonautonomous system of two linear differential equations: , , where the matrix-valued function has a kind of singularity at . It is called rectifiable (resp., nonrectifiable) attractivity of the zero solution, which means that as and the length of the solution curve of is finite (resp., infinite) for every . It is characterized in terms of certain asymptotic behaviour of the eigenvalues of near . Consequently, the main results are applied to a system of two linear differential equations with polynomial coefficients which are singular at .