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The investigation of bounded solutions to systems of differential equations involve some important and challenging problems of perturbation theory of invariant toroidal manifolds. Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology and this monograph is a detailed study of the application of Lyapunov functions with variable sign, expressed in quadratic forms to the solution of problems including; preservation of invariant tori of dynamic systems under perturbation. The volume is a classic contribution to the literature on stability theory and provides a useful source of reference for postgraduates and researchers.
Asymptotic Methods in Resonance Analytical Dynamics presents new
asymptotic methods for the analysis and construction of solutions
(mainly periodic and quasiperiodic) of differential equations with
small parameters. Along with some background material and theory
behind these methods, the authors also consider a variety of
problems and applications in nonlinear mechanics and oscillation
theory. The methods examined are based on two types: the
generalized averaging technique of Krylov-Bogolubov and the
numeric-analytical iterations of Lyapunov-PoincarA(c). This text
provides a useful source of reference for postgraduates and
researchers working in this area of applied mathematics.
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