Methods In Equivariant Bifurcations And Dynamical Systems
Seiten
2000
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-3828-5 (ISBN)
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-3828-5 (ISBN)
An introduction to bifurcation theory in the presence of symmetry. It aims to expound the mathematical methods of equivariant bifurcation theory and present the most recent ideas and results in this theory, in relation to applications. There are exercises at the end of each chapter.
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.
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.
Symmetries in ODEs and PDEs; equivariant bifurcations, a first look; invariant manifolds and normal forms; linear Lie group actions; the equivariant structure of bifurcation equations; reduction techniques for equivariant systems; relative equilibria and relative periodic orbits; bifurcations in equivariant systems; heteroclinic cycles; perturbation of equivariant systems.
| Erscheint lt. Verlag | 1.3.2000 |
|---|---|
| Reihe/Serie | Advanced Series in Nonlinear Dynamics ; 15 |
| Verlagsort | Singapore |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik | |
| ISBN-10 | 981-02-3828-2 / 9810238282 |
| ISBN-13 | 978-981-02-3828-5 / 9789810238285 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 83,90
