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Mathematical symmetry and chaos come together to form striking, beautiful color images throughout this impressive work, which addresses how the dynamics of complexity can produce familiar universal patterns. The book, a richly illustrated blend of mathematics and art, was widely hailed in publications as diverse as the New York Review of Books, Scientific American, and Science when first published in 1992. This much-anticipated second edition features... more...

Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. The nature of these changes depends both on the number of parameters and on the symmetries of the equations. Volume I discusses how singularity-theoretic techniques aid the understanding of transitions in multiparameter systems. This volume focuses on bifurcation problems with symmetry and shows how group-theoretic techniques aid the understanding... more...

This IMA Volume in Mathematics and its Applications PATTERN FORMATION IN CONTINUOUS AND COUPLED SYSTEMS is based on the proceedings of a workshop with the same title, but goes be­ yond the proceedings by presenting a series of mini-review articles that sur­ vey, and provide an introduction to, interesting problems in the field. The workshop was an integral part of the 1997-98 IMA program on "EMERG­ ING APPLICATIONS OF DYNAMICAL SYSTEMS." I would... more...

Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. The nature of these changes depends both on the number of parameters and on the symmetries of the equations. Volume I discusses how singularity-theoretic techniques aid the understanding of transitions in multiparameter systems. This volume focuses on bifurcation problems with symmetry and shows how group-theoretic techniques aid the understanding... more...

Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. The nature of these changes depends both on the number of parameters and on the symmetries of the equations. Volume I discusses how singularity-theoretic techniques aid the understanding of transitions in multiparameter systems. This volume focuses on bifurcation problems with symmetry and shows how group-theoretic techniques aid the understanding... more...

Symmetry is one of the most powerful and wide-ranging of mathematical ideas with recent work on symmetry breaking, when symmetrical patterns are slightly altered or corrupted, throwing up an extraordinary range of applications and natural examples, from the stripes on a tiger's back to the territorial patterns of fish and to the structure of viruses. This book looks at the applications of symmetry and symmetry breaking to subjects as diverse as weather... more...