On some clarifications of estimates of Lyapunov’s exponents in the method of freezing

Abstract

Abstract Method of V.M. Alekseev was used to obtain the clarifications of lower estimates for the lower singular exponent and of upper estimates for the upper singular exponent of a linear system of differential equations. In contrast to the classical results of the freezing method, which assume that the derivatives of the elements of the matrix of the coefficients of the system are small, the new estimates admit that these derivatives are unbounded.