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.
The Princeton Legacy Library uses the latest print-on-demand
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the distinguished backlist of Princeton University Press. These editions
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them in durable paperback and hardcover editions. The goal of the
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scholarly heritage found in the thousands of books published by
Princeton University Press since its founding in 1905.
