Lyapunov exponents as functions of a parameter

The author proves the typical nature, in the sense of Baire category, of the upper semicontinuity of the Lyapunov exponents of a family of endomorphisms of a metrized vector bundle, considered as a function of a parameter on which a point of the base of this bundle continuously depends. It is proved that the Lyapunov exponents, as functions of this parameter, belong to the second Baire class. An application of these abstract theorems to the Lyapunov exponents of nonlinear systems of differential equations continuously depending on a parameter is given.
Bibliography: 14 titles.