
Lectures on Bifurcations, Dynamics and Symmetry
Michael Field(Author)
CRC Press
1st Edition
Published on 18. December 2020
Book
Hardback
168 pages
978-1-138-41764-9 (ISBN)
Description
This book is an expanded version of a Master Class on the symmetric bifurcation theory of differential equations given by the author at the University of Twente in 1995. The notes cover a wide range of recent results in the subject, and focus on the dynamics that can appear in the generic bifurcation theory of symmetric differential equations. Many of the results and examples in the book are new and have not been previously published. The first four chapters contain an accessible presentation of the fundamental work by Field and Richardson on symmetry breaking and the Maximal Isotropy Subgroup Conjecture. The remainder of the book focuses on recent research of the author and includes chapters on the invariant sphere theorem, coupled cell systems, heteroclinic cycles , equivariant transversality, and an Appendix (with Xiaolin Peng) giving a new low dimensional counterexample to the converse of the Maximal Isotropy Subgroup Conjecture. The chapter on coupled cell systems includes a weath of new examples of 'cycling chaos'. The chapter on equivariant transversality is introductory and centres on an extended discussion of an explicit system of four coupled nonlinear oscillators. The style and format of the original lectures has largely been maintained and the notes include over seventy exercises with hints for solutions and suggestions kfor further reading). In general terms, the notes are directed at mathematicians and aplied scientists working in the field of bifurcation theory who wish to learn about some of the latest developments and techniques in equivariant bifurcation theory. The notes are relatively self-contained and are structured so that they can form the basis for a graduate level course in equivariant bifurcation theory.
More details
Series
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
Professional and scholarly
Professional
Dimensions
Height: 246 mm
Width: 170 mm
Weight
470 gr
ISBN-13
978-1-138-41764-9 (9781138417649)
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Schweitzer Classification
Other editions
Additional editions

Michael Field
Lectures on Bifurcations, Dynamics and Symmetry
E-Book
02/2020
1st Edition
Chapman & Hall/CRC
€172.99
Available for download

Michael Field
Lectures on Bifurcations, Dynamics and Symmetry
E-Book
02/2020
1st Edition
Chapman & Hall/CRC
€172.99
Available for download

Michael Field
Lectures on Bifurcations, Dynamics and Symmetry
Book
09/1996
1st Edition
CRC Press
€160.94
Article not available at the moment
Person
Michael J. Field
Content
Chapter 1. Introduction & preliminaries, Chapter 2. Hyperoctahedral groups, Chapter 3. A zoo of bifurcations, Chapter 4. Stability and determinacy, Chapter 5. The invariant sphere theorem, Chapter 6. Heteroclinic cycles in equivariant bifurcations, Chapter 7. Symmetrically coupled cell systems, Chapter 8. An example of Z2-transversality in a system of four coupled oscillators, Chapter 9. Geometric methods, Appendix A. Converse to the MISC, Hints and solutions to selected exercises, Bibliography, Index