N. A. Izobov. Institute of Mathematics
National Academy of Sciences of Belarus, Minsk
The monograph contains the necessary information from the modern theory
of Lyapunov characteristic exponents of ordinary linear differential systems.
It is mainly dedicated to the brief description of the results obtained by the
author, connected with the development of the following parts: the theory
of Perron lower exponents, the freezing method, the theory of exponential
and sigma-exponents and their connection with characteristic, central,
and general exponents, the dependence of characteristic exponents of linear
systems on exponentially decreasing perturbation and the theory of their
stability with respect to small perturbations. As an application of those
results the author considered the Lyapunov problem on the exponential
stability of an ordinary differential system by linear approximation. In the
monograph the method of rotations by V.M.Millionschikov is systematically
used. This volume is intended for specialists in the asymptotic theory of
ordinary differential systems and the stability theory, for post-graduates
and students specialized in the field of differential equations.