Frequency-Domain Methods for Nonlinear Analysis: Theory and Applications (World Scientific Nonlinear Science Series a)

Leonov, Gennady A, Ponomarenko, Dimitrij V, Smirnova, V B

ISBN 10: 9810221460 / ISBN 13: 9789810221461

Published by World Scientific Publishing Company, 1996

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Bibliographic Details

• Title: Frequency-Domain Methods for Nonlinear Analysis: Theory and Applications (World Scientific Nonlinear Science Series a)
• Publisher: World Scientific Publishing Company
• Publication Date: 1996
• Language: English
• ISBN 10: 9810221460
• ISBN 13: 9789810221461
• Binding: Hardcover
• Condition: Very Good
• Dust Jacket Condition: Dust Jacket Included
• Book Type: book

About this title

Synopsis

This book deals with the investigation of global attractors of nonlinear dynamical systems. The exposition proceeds from the simplest attractor of a single equilibrium to more complicated ones, i.e. to finite, denumerable and continuum equilibria sets; and further, to cycles, homoclinic and heteroclinic orbits; and finally, to strange attractors consisting of irregular unstable trajectories. On the complicated equilibria sets, the methods of Lyapunov stability theory are transferred. They are combined with stability techniques specially elaborated for such sets. The results are formulated as frequency-domain criteria. The methods connected with the theorems of existence of cycles and homoclinic orbits are developed. The estimates of Hausdorff dimensions of attractors are presented.