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
technology to again make available previously out-of-print books
from the distinguished backlist of Princeton University Press.
These paperback editions preserve the original texts of these
important books while presenting them in durable paperback
editions. The goal of the Princeton Legacy Library is to vastly
increase access to the rich scholarly heritage found in the
thousands of books published by Princeton University Press since
its founding in 1905.
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