Multifrequency Oscillations of Nonlinear Systems / Edition 1

by Anatolii M. Samoilenko, R. Petryshyn

Overview

In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies. In the process of evolution, systems of this type can pass from one resonance state into another. This fact considerably complicates the investigation of nonlinear oscillations.

In the present monograph, a new approach based on exact uniform estimates of oscillation integrals is proposed. On the basis of this approach, numerous completely new results on the justification of the averaging method and its applications are obtained and the integral manifolds of resonance oscillation systems are studied.

This book is intended for a wide circle of research workers, experts, and engineers interested in oscillation processes, as well as for students and post-graduate students specialized in ordinary differential equations.

Product Details

ISBN-13:	9781402020308
Publisher:	Springer Netherlands
Publication date:	07/28/2004
Series:	Mathematics and Its Applications , #567
Edition description:	2004
Pages:	317
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Averaging Method in Oscillation Systems with Variable Frequencies.- Aceraging Method in Multipoint Problems.- Integral Manifolds.- Investigation of a Dynamical System in a Neighborhood of a Quasiperiodic Trajectory.

Editorial Reviews

From the reviews:

"The present research monograph deals with the averaging method for multifrequency nonlinear systems of ordinary differential equations. It gives a careful and detailed exposition to recent achievements by the authors and their coworkers based on exact uniform estimates of oscillatory integrals. As a result, many new results on the justification of the averaging method and its applications are obtained ... ." (G. Teschl, Monashefte für Mathematik, Vol. 146 (2), 2005)

From the Publisher