On simplified formulas for the central exponents of differential systems with non-uniform scales

We study the Vinograd–Millionshchikov central exponents, which represent the exact outer boundaries for the mobility of the extremal values of the Lyapunov and Perron exponents of a linear differential system under uniformly small perturbations of its coefficients. We prove the possibility of calculating those exponents using simplified formulas with expanding time scales and obtain concrete estimates of the central exponents with simplified ones, calculated in different scales: thick, expanding, slowly expanding and sparse.