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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. [ABSTRACT FROM AUTHOR]

For parametric families of n-dimensional linear differential systems on the time semiaxis with parameter varying in a metric space, we consider two functions of the parameter defined as the dimension of the subspace of solutions that have the characteristic exponent that, respectively, is less than or does not exceed a given real number. A complete description is derived both for the functions themselves and for the vector function composed of them, for the families of systems continuous in one of the two topologies: uniform or compact-open. In addition, the Lebesgue sets and the sets of points of upper and lower semicontinuity are described for the indicated functions. [ABSTRACT FROM AUTHOR]

We consider families of n-dimensional (n ≥ 2) linear differential systems on the time semiaxis with parameter varying in a metric space. For such families continuously depending on the parameter in the sense of uniform convergence on the time semiaxis, we completely describe the spectra of their Lyapunov exponents as vector functions of the parameter. [ABSTRACT FROM AUTHOR]