Bifurcation, Symmetry and Patterns

✍ Scribed by Ian Stewart, Toby Elmhirst, Jack Cohen (auth.), Jorge Buescu, Sofia B. S. D. Castro, Ana Paula da Silva Dias, Isabel Salgado Labouriau (eds.)

Publisher: Birkhäuser Basel
Year: 2003
Tongue: English
Leaves: 214
Series: Trends in Mathematics
Edition: 1
Category: Library

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✦ Synopsis

This book represents the latest developments on both the theory and applications of bifurcations with symmetry. It includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern mathematics at the same time as it contains work of young mathematicians in new directions. The range of topics includes mathematical biology, pattern formation, ergodic theory, normal forms, one-dimensional dynamics and symmetric dynamics.

✦ Table of Contents

Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Symmetry-Breaking as an Origin of Species....Pages 3-54
Bifurcation and Planar Pattern Formation for a Liquid Crystal....Pages 55-66
Patchwork Patterns: Dynamics on Unbounded Domains....Pages 67-74
Persistent Ergodicity and Stably Ergodic SRB Attractors in Equivariant Dynamics....Pages 75-86
Bistability of Vortex Modes in Annular Thermoconvection....Pages 87-99
Secondary Instabilities of Hexagons: A Bifurcation Analysis of Experimentally Observed Faraday Wave Patterns....Pages 101-114
Front Matter....Pages 115-115
Spatially Resonant Interactions in Annular Convection....Pages 117-122
Hopf Bifurcations on Cubic Lattices....Pages 123-127
Normal Forms of Dynamical Systems and Bifurcations....Pages 129-134
One-dimensional Pattern Formation in Systems with a Conserved Quantity....Pages 135-140
Invariance and Symmetry in a Year-class Model....Pages 141-150
The Accumulation of Boundary Doubling for Modified Tent Maps....Pages 151-155
Piecewise Rotations: Bifurcations, Attractors and Symmetries....Pages 157-165
Bound States of Asymmetric Hot Spots in Solid Flame Propagation....Pages 167-174
Pattern Formation with Galilean Symmetry....Pages 175-180
Semigroups of Functions and the Structure of Stationary Measures in Systems which Contract-on-average....Pages 181-187
Rayleigh-Bénard Convection with Experimental Boundary Conditions....Pages 189-195
Global Bifurcations in FitzHugh-Nagumo Model....Pages 197-202
Back Matter....Pages 203-210

✦ Subjects

Dynamical Systems and Ergodic Theory

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