Complete description of the Lyapunov spectra of continuous families of linear differential systems withunbounded coefficients

For every positive integer $n$ and every metric space $M$ we consider the class$\widetilde{\mathcal{U}}^n(M)$ of all parametric families $\dot x = A(t, \mu)x$, where $x\in\mathbb{R}^n$, $t\ge 0$,$\mu\in M$, of linear differential systems whose coefficients are piecewise continuous and, generally speaking,unbounded on the time semi-axis for every fixed value of the parameter $\mu$ such that if a sequence$(\mu_k)$ converges to $\mu_0$ in the space of parameters, then the sequence $(A( {\cdot} ,\mu_k))$\linebreakconverges uniformly on the semi-axis to the matrix $A( {\cdot} ,\mu_0)$. For the familiesin $\widetilde{\mathcal{U}}^n(M)$, we obtain a complete description of individual Lyapunov exponents andtheir spectra as functions of the parameter.

linear differential system, Lyapunov exponents, infinitesimal perturbations, Baire classes