Functions Determined by the Lyapunov Exponents of Families of Linear Differential Systems Continuously Depending on the Parameter Uniformly on the Half-Line

Abstract

For families of n-dimensional linear differential systems (n ≥ 2) whose dependence on a parameter ranging in a metric space is continuous in the sense of the uniform topology on the half-line, we obtain a complete description of the ith Lyapunov exponent as a function of the parameter for each i = 1,..., n. As a corollary, we give a complete description of the Lebesgue sets and (in the case of a complete separable parameter space) the range of an individual Lyapunov exponent of such a family.