Lyapunov Irregularity Coefficient as a Function of the Parameter for Families of Linear Differential Systems Whose Dependence on the Parameter Is Continuous Uniformly on the Time Half-Line

Abstract

We consider families of n-dimensional (n ≥ 2) linear differential systems on the time half-line with parameter belonging to a metric space. We obtain a complete description of the Lyapunov irregularity coefficient as a function of the parameter for families whose dependence on the parameter is continuous in the sense of uniform convergence on the time half-line. As a corollary, we completely describe the parametric dependence of the Lyapunov irregularity coefficient of a regular linear system with a linear parametric perturbation decaying at infinity uniformly with respect to the parameter.