Instabilities and fronts in extended systems / Pierre Collet, Jean-Pierre Eckmann

Collet, Pierre (1948-)

ISBN 10: 0691085684 / ISBN 13: 9780691085685

Published by Princeton, New Jersey : Princeton University Press, 1990

About this Item

Fine cloth copy in an equally fine dust-wrapper. Particularly well-preserved overall; tight, bright, clean and especially sharp-cornered. Physical description: 209 pages : illustrations. Subject: Bifurcation theory. Stability. Differentiable dynamical systems. SCIENCE Physics General. 1 Kg.

Seller Inventory # 383495

Bibliographic Details

• Title: Instabilities and fronts in extended systems / Pierre Collet, Jean-Pierre Eckmann
• Publisher: Princeton, New Jersey : Princeton University Press
• Publication Date: 1990
• Language: English
• ISBN 10: 0691085684
• ISBN 13: 9780691085685
• Binding: Hardcover
• Edition: First Edition.
• Weight: 1 kilogram

About this title

Synopsis

The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on this subject in which solutions, bifurcations, fronts, and the dynamical stability of these objects are discussed. To the uninitiated reader, the theoretical methods that lead to the various results often seem somewhat ad hoc, and it is not clear how to generalize them to the nextthat is, not yet solvedproblem. In an introduction to the subject of instabilities in spatially infinite systems, Pierre Collet and Jean-Pierre Eckmann aim to give a systematic account of these methods, and to work out the relevant features that make them operational. The book examines in detail a number of model equations from physics. The mathematical developments of the subject are based on bifurcation theory and on the theory of invariant manifolds. These are combined to give a coherent description of several problems in which instabilities occur, notably the Eckhaus instability and the formation of fronts in the Swift-Hohenberg equation. These phenomena can appear only in infinite systems, and this book breaks new ground as a systematic account of the mathematics connected with infinite space domains.

Originally published in 1990.

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Synopsis

Rather densely mathematical monograph in which the authors (made familiar to many by their collaborative Iterated maps on the interval as dynamical systems 1980) explore some difficult aspects of the physics of distributed systems, i.e., of physical systems described by partial differential equations. The work pertains (but not exclusively) to the