Pascal Chossat's Books

Methods In Equivariant Bifurcations And Dynamical Systems

By: Pascal Chossat,Reiner Lauterbach

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Methods In Equivariant Bifurcations And Dynamical Systems

By: Pascal Chossat,Reiner Lauterbach

This invaluable book presents a comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably over the past twenty years and has been very successful in analysing and predicting pattern formation and other critical phenomena in most areas of science where nonlinear models are involved, like fluid flow instabilities, chemical waves, elasticity and population dynamics.The book has two aims. One is to expound the mathematical methods of equivariant bifurcation theory. Beyond the classical bifurcation tools, such as center manifold and normal form reductions, the presence of symmetry requires the introduction of the algebraic and geometric formalism of Lie group theory and transformation group methods. For the first time, all these methods in equivariant bifurcations are presented in a coherent and self-consistent way in a book.The other aim is to present the most recent ideas and results in this theory, in relation to applications. This includes bifurcations of relative equilibria and relative periodic orbits for compact and noncompact group actions, heteroclinic cycles and forced symmetry-breaking perturbations. Although not all recent contributions could be included and a choice had to be made, a rather complete description of these new developments is provided. At the end of every chapter, exercises are offered to the reader.

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Page Count

422

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813105445

ISBN 13

9789813105447

The Couette-Taylor Problem

By: Pascal Chossat,Gerard Iooss

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The Couette-Taylor Problem

By: Pascal Chossat,Gerard Iooss

1. 1 A paradigm About one hundred years ago, Maurice Couette, a French physicist, de signed an apparatus consisting of two coaxial cylinders, the space between the cylinders being filled with a viscous fluid and the outer cylinder being rotated at angular velocity O2. The purpose of this experiment was, follow ing an idea of the Austrian physicist Max Margules, to deduce the viscosity of the fluid from measurements of the torque exerted by the fluid on the inner cylinder (the fluid is assumed to adhere to the walls of the cylinders). At least when O is not too large, the fluid flow is nearly laminar and 2 the method of Couette is valuable because the torque is then proportional to 110 , where II is the kinematic viscosity of the fluid. If, however, O is 2 2 increased to a very large value, the flow becomes eventually turbulent. A few years later, Arnulph Mallock designed a similar apparatus but allowed the inner cylinder to rotate with angular velocity 01, while O2 = o. The surprise was that the laminar flow, now known as the Couette flow, was not observable when 0 exceeded a certain "low" critical value Ole, even 1 though, as we shall see in Chapter II, it is a solution of the model equations for any values of 0 and O .

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Page Count

239

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461243009

ISBN 13

9781461243007

Methods In Equivariant Bifurcations And Dynamical Systems

By: Pascal Chossat,Reiner Lauterbach

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Methods In Equivariant Bifurcations And Dynamical Systems

By: Pascal Chossat,Reiner Lauterbach

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Solve jigsaw puzzle

Age

Page Count

422

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813105445

ISBN 13

9789813105447

The Couette-Taylor Problem

By: Pascal Chossat,Gerard Iooss

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The Couette-Taylor Problem

By: Pascal Chossat,Gerard Iooss

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

239

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461243009

ISBN 13

9781461243007

Book's by Pascal Chossat

Methods In Equivariant Bifurcations And Dynamical Systems

Methods In Equivariant Bifurcations And Dynamical Systems

The Couette-Taylor Problem

The Couette-Taylor Problem

Methods In Equivariant Bifurcations And Dynamical Systems

Methods In Equivariant Bifurcations And Dynamical Systems

The Couette-Taylor Problem

The Couette-Taylor Problem

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