Averaging in Stability Theory: A Study of Resonance Multi-Frequency Systems [Paperback]

1 Averaging of Ordinary Differential Equations in One  and Multi  Frequency Systems.- 1.1 Introduction.- 1.2 Averaging in Standard  Form Systems.- 1.3 Averaging in Systems with Slow and Fast Variables.- 1.4 Averaging in Multi  Frequency Systems.- 2 Generalization of Lyapunov Second Method and Averaging in Stability Theory.- 2.1 Introduction.- 2.2 Lyapunov Functions Positive  Definite in Subset of Variables.- 2.3 Equipotential Surfaces of Perturbed Lyapunov Function. Proximity of Solutions of Complete and Unperturbed Systems.- 2.4 Perturbed Lyapunov Function in Annular Region. Theorem on Stability.- 2.5 Theorem on Attraction of Solutions to Equilibrium Point.- 2.6 Investigation of Stability on Finite Interval.- 2.7 Investigation of Stability in Higher Approximations.- 2.8 Theorem on Asymptotic Stability of Perturbed Nonlinear Systems in Neutral Case.- 2.9 Theorems on Asymptotic Stability of Standard  Form Systems and Systems with Small Perturbations.- 2.10 Theorem on Stability of Systems Splitting without Perturbations.- 2.11 Stability of Systems with Additional Correlations between Properties of Mean and Derivative of Lyapunov Function.- 2.12 Investigation of Stability by Averaging over Explicit Time Dependence.- 2.13 Investigation of Stability by Averaging along Solutions of Linear System.- 2.14 Investigation of Stability of Integro  Differential Systems.- 2.15 On Numerical Realization of Theorems of Generalized Lyapunov Second Method.- 2.16 Theorems on Instability.- 2.17 Study of Stability of Perturbed Systems Using Positive  Definite Function which is not Lyapunov Function.- 3 Stability of Systems of Ordinary Differential Equations with Quasi  Periodic Coefficients.- 3.1 Investigation of Stability by Means of Lyapunov Function of LinearSystem.- 3.2 Construction of Perturbed Lyapunov Function for Higher Order Resonances.- 4 Stability of Multi  Frequency Systems 114.- 4.1 Statement of the Problem.- 4.2 Stability of Single  Frequency Systems of Equations lC1