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Download or read book Dichotomies and Stability in Nonautonomous Linear Systems written by Yu. A. Mitropolsky and published by CRC Press. This book was released on 2002-10-10 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.