http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Dichotomies and stability in nonautonomous linear systems
Samoĭlenko, A. M. (Anatoliĭ Mikhaĭlovich)
Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov functions with variable sign, expressed in quadratic forms, to the solution of this problem. The authors explore the preservation of invariant tori of dynamic systems under perturbation. This volume is a classic contribution to the literature on stability theory and provides a useful source of reference for postgraduates and researchers.
chapter 1 Exponentially Dichotomous Linear Systems of Differential Equations and Lyapunov Functions of Variable Sign -- chapter 2 Linear Extension of Dynamical Systems on a Torus -- chapter 3 Splittability of Linear Extensions of Dynamical Systems on a Torus -- chapter 4 Problems of Perturbation Theory of Smooth Invariant Tori of Dynamical Systems.
by Yu. A. Mitropolsky, A.M. Samoilenko and V.L. Kulik.
Stability and control: theory, methods and applications