Pattern Formation

by Chadam, John; Golubitsky, Martin; Langford, William; Wetton, Brian

• ISBN13: 9780821802564
• ISBN10: 0821802569
• Format: Hardcover
• Copyright: 1995-11-01
• Publisher: Amer Mathematical Society

Summary

This volume covers the spectrum of research involved in combining symmetry methods with dynamical systems and bifurcation theory, from the development of the mathematical theory to partial differential equation models of realistic physical phenomena. The individual contributions show the richness of the interplay between abstract methods and significant essential examples.

Table of Contents

Towards analyzing the dynamics of flames

Symmetries in modulated traveling waves in combustion: Jumping ponies on a merry-go-round

Modulated traveling waves for the Kuramoto-Sivashinsky equation

Length scales in phase transition models: Phase field, Cahn-Hilliard, and blow-up problems

Veronese and the detectives: Finding the symmetry of attractors

$D_4$-symmetric maps with hidden Euclidean symmetry

Modelling travelling waves of spatial patterning in morphogenesis

Analysis of models of pancreatic$\beta$-cells exhibiting temporal pattern formation

Translating patterns in a generalized Ginzburg-Landau amplitude equation

Geometric methods in bifurcation theory

Secondary Hopf bifurcation caused by steady-state steady-state mode interaction

Symmetry breaking bifurcations in spherical Benard convection. Part I: Results from singularity theory

Symmetry breaking bifurcations in spherical Benard convection. Part II: Numerical results

On a dynamical model for phase transformation in nonlinear elasticity

System symmetry breaking and Shilnikov dynamics

Generalizations of a result on symmetry groups of attractors

Instabilities induced by differential flows

Self-organized zoning in crystals: Free boundaries, matched asymptotics, and bifurcaton

Some aspects of successive bifurcations in the Couette-Taylor problem

Bifurcating waves in coupled cells described by delay-differential equations

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