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 of transitions in symmetric systems. Four broad topics are covered: group theory and steady-state bifurcation, equicariant singularity theory, Hopf bifurcation with symmetry, and mode interactions. The opening chapter provides an introduction to these subjects and motivates the study of systems with symmetry. Detailed case studies illustrate how group-theoretic methods can be used to analyze specific problems arising in applications.
Singularities and Groups in Bifurcation Theory
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1 of 1 people found the following review helpful:
5.0 out of 5 stars
Excellent introduction to bifurcation theory with symmetries,
This review is from: Singularities and Groups in Bifurcation Theory: Volume 2 (Applied Mathematical Sciences) (Hardcover)
This book provides an efficient and understandable introduction to bifurcation from fixed points in systems with symmetries. Several well established physical examples, which are the focus of active research, are discussed and further references given. It is a must for anyone interested in the subject.
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Inside This Book
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First Sentence:
In Volume I we showed how techniques from singularity theory may be applied to bifurcation problems, and how complicated arrangements of bifurcations may be studied by unfolding degenerate singularities. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
commuting linear mappings, universal unfolding theorem, equivariant singularity theory, maximal isotropy subgroups, midplane reflection, intermediate order terms, normal form commutes, equivariant branching lemma, twisted subgroups, imaginary eigenspace, isotropy lattice, infinite cylinder approximation, third order truncation, topological codimension, branching equations, singularity theory analysis, disjoint union decompositions, modulo higher order terms, planar subgroups, reduced bifurcation equations, orbital asymptotic stability, nonlinear degeneracies, nonstandard actions, commuting mappings, mixed mode solutions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Group-Theoretic Preliminaries, Equivariant Unfolding Theory, The Planar Bénard Problem, Oscillations of Identical Cells Coupled New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In Volume I we showed how techniques from singularity theory may be applied to bifurcation problems, and how complicated arrangements of bifurcations may be studied by unfolding degenerate singularities. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
commuting linear mappings, universal unfolding theorem, equivariant singularity theory, maximal isotropy subgroups, midplane reflection, intermediate order terms, normal form commutes, equivariant branching lemma, twisted subgroups, imaginary eigenspace, isotropy lattice, infinite cylinder approximation, third order truncation, topological codimension, branching equations, singularity theory analysis, disjoint union decompositions, modulo higher order terms, planar subgroups, reduced bifurcation equations, orbital asymptotic stability, nonlinear degeneracies, nonstandard actions, commuting mappings, mixed mode solutions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Group-Theoretic Preliminaries, Equivariant Unfolding Theory, The Planar Bénard Problem, Oscillations of Identical Cells Coupled New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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3
books
cite this book:
- Systems of Nonlinear Partial Differential Equations (NATO Science Series C: (closed)) by J.M. Ball in Back Matter (1), and Back Matter (2)
- Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences Vol. 42) by John Guckenheimer in Front Matter, and Back Matter
- Applications of Centre Manifold Theory (Applied Mathematical Sciences) by J. Carr in Front Matter, and Back Matter
- Partial Differential Equations and Dynamical Systems (Research notes in mathematics 101) by William E. Fitzgibbon in Back Matter (1), and Back Matter (2)
- Ordinary Differential Equations (Universitext) by Vladimir I. Arnold in Back Matter
See all 100 books this book cites
- Dynamic Modelling, Bifurcation and Chaotic Behaviour of Gas-Solid Catalytic Reactors (Topics in Chemical Engineering) by S. S. E. H. Elnashaie in Back Matter
- Singularities (London Mathematical Society Lecture Note Series) by Jean-Paul Brasselet on page 284
- Global Analysis of Dynamical Systems by H.W Broer on page 306
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