Instabilities and Fronts in Extended Systems
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A01=Jean-Pierre Eckmann
A01=Pierre Collet
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Asymptotic analysis
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Author_Jean-Pierre Eckmann
Author_Pierre Collet
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Banach space
Bifurcation diagram
Bifurcation theory
Bloch function
Boundary problem (spatial analysis)
Boundary value problem
Bounded operator
Calculation
Catastrophe theory
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Cauchy problem
Cauchy sequence
Change of variables
Chaos theory
Codimension
Coefficient
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Complex number
Conjugate transpose
Continuous spectrum
Convolution
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Derivative
Diffeomorphism
Differential equation
Differential operator
Dimension (vector space)
Dynamical system
Eigenfunction
Eigenplane
Eigenvalues and eigenvectors
Elliptic operator
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Equation
Equilibrium point
Essential spectrum
Even and odd functions
Existential quantification
Extrapolation
Forcing (recursion theory)
Formal power series
Free boundary problem
Fréchet derivative
Function space
Homeomorphism
Hopf bifurcation
Initial condition
Initial value problem
Integration by parts
Invariant manifold
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Limit cycle
Linear map
Linear stability
Linearization
Oscillation
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Parameter
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Perturbation theory (quantum mechanics)
Phase space
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Pseudo-differential operator
Quasiperiodic function
Sobolev inequality
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Submanifold
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Time evolution
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Product details
- ISBN 9780691607610
- Weight: 369g
- Dimensions: 178 x 254mm
- Publication Date: 14 Jul 2014
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
- Language: English
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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 editions preserve the original texts of these important books while presenting them in durable paperback and hardcover 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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