Nonlinear differential equations and dynamical systems.

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Last edited by MARC Bot
September 28, 2024 | History

Nonlinear differential equations and dynamical systems.

On the subject of differential equations a great many elementary books have been written. This book bridges the gap between elementary courses and the research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed. Stability theory is developed starting with linearisation methods going back to Lyapunov and Poincaré. The global direct method is then discussed. To obtain more quantitative information the Poincaré-Lindstedt method is introduced to approximate periodic solutions while at the same time proving existence by the implicit function theorem. The method of averaging is introduced as a general approximation-normalisation method. The last four chapters introduce the reader to relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, Hamiltonian systems (recurrence, invariant tori, periodic solutions). The book presents the subject material from both the qualitative and the quantitative point of view. There are many examples to illustrate the theory and the reader should be able to start doing research after studying this book.

Publish Date
Publisher
Springer-Verlag
Language
English
Pages
277

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Previews available in: English

Book Details


Edition Notes

Includes bibliographical references.

Published in
Berlin, London
Series
Universitext

Classifications

Library of Congress
QA372 .V47 1990, QA299.6-433

Edition Identifiers

Open Library
OL15275349M
Internet Archive
nonlineardiffere0000verh
ISBN 10
3540506284
LCCN
89021770

Work Identifiers

Work ID
OL8055441W

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September 28, 2024 Edited by MARC Bot import existing book
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December 3, 2010 Edited by Open Library Bot Added subjects from MARC records.
December 10, 2009 Created by WorkBot add works page