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 .
"Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations." Int. J. Differ. Equ. 2013 (SI2) 1 - 11, 2013. https://doi.org/10.1155/2013/740980