engleski

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

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 zaro. 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). It is characterized in terms of certain asymptotic behaviour of the eigenvalues of near t=0. Consequently, the main results are applied to a system of two linear differential equations with polynomial coefficients which are singular at t=0.

nonautonomous system ; rectifiability ; attractivity ; zero solution

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