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This volume presents a generalization of the second Lyapunov method involving its combination with the asymptotic averaging method. This generalized method can be applied to multifrequency systems having resonance harmonics. A new method is also described for estimating small denominators in multifrequency systems which makes use of the nonlinear properties of the system frequencies. The methods derived can also be extended to integro-differential equations, delay differential equations, and to partial differential equations having small nonlinear terms. One of the various applications relating to multifrequency and resonance problems which are discussed in this book is the stability of the classical three-body problem. For specialists in stability theory, nonlinear oscillation theory and asymptotic methods in mathematics and celestial mechanics.
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