Structure of the sets of points of semicontinuity for the Lyapunov exponents of linear systems continuously depending on a parameter in the uniform norm on the half-line

Abstract

For a family of n-dimensional (n ≥ 2) linear differential systems depending continuously, in the sense of the uniform norm on the half-line, on a parameter varying in a complete metric space, we obtain a complete description of the sets of points of lower semicontinuity and upper semicontinuity of the ith Lyapunov exponent, i = 1,..., n, treated as a function of the parameter.