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Author:   Martin Golubitsky ,  Ian Stewart
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2002 ed.
Volume:   200
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   1.470kg
ISBN:  

9783764366094

ISBN 10:   3764366095
Pages:   325
Publication Date:   01 January 2002
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

1. Steady-State Bifurcation.- 1.1. Two Examples.- 1.2. Symmetries of Differential Equations.- 1.3. Liapunov-Schmidt Reduction.- 1.4. The Equivariant Branching Lemma.- 1.5. Application to Speciation.- 1.6. Observational Evidence.- 1.7. Modeling Issues: Imperfect Symmetry.- 1.8. Generalization to Partial Differential Equations.- 2. Linear Stability.- 2.1. Symmetry of the Jacobian.- 2.2. Isotypic Components.- 2.3. General Comments on Stability of Equilibria.- 2.4. Hilbert Bases and Equivariant Mappings.- 2.5. Model-Independent Results for D3Steady-State Bifurcation.- 2.6. Invariant Theory for SN.- 2.7. Cubic Terms in the Speciation Model.- 2.8. Steady-State Bifurcations in Reaction-Diffusion Systems.- 3. Time Periodicity and Spatio-Temporal Symmetry.- 3.1. Animal Gaits and Space-Time Symmetries.- 3.2. Symmetries of Periodic Solutions.- 3.3. A Characterization of Possible Spatio-Temporal Symmetries.- 3.4. Rings of Cells.- 3.5. An Eight-Cell Locomotor CPG Model.- 3.6. Multifrequency Oscillations.- 3.7. A General Definition of a Coupled Cell Network.- 4. Hopf Bifurcation with Symmetry.- 4.1. Linear Analysis.- 4.2. The Equivariant Hopf Theorem.- 4.3. Poincaré-Birkhoff Normal Form.- 4.4. ?(2) Phase-Amplitude Equations.- 4.5. Traveling Waves and Standing Waves.- 4.6. Spiral Waves and Target Patterns.- 4.7. ?(2) Hopf Bifurcation in Reaction-Diffusion Equations.- 4.8. Hopf Bifurcation in Coupled Cell Networks.- 4.9. Dynamic Symmetries Associated to Bifurcation.- 5. Steady-State Bifurcations in Euclidean Equivariant Systems.- 5.1. Translation Symmetry, Rotation Symmetry, and Dispersion Curves.- 5.2. Lattices, Dual Lattices, and Fourier Series.- 5.3. Actions on Kernels and Axial Subgroups.- 5.4. Reaction-Diffusion Systems.- 5.5. Pseudoscalar Equations.- 5.6. The Primary VisualCortex.- 5.7. The Planar Bénard Experiment.- 5.8. Liquid Crystals.- 5.9. Pattern Selection: Stability of Planforms.- 6. Bifurcation From Group Orbits.- 6.1. The Couette-Taylor Experiment.- 6.2. Bifurcations From Group Orbits of Equilibria.- 6.3. Relative Periodic Orbits.- 6.4. Hopf Bifurcation from Rotating Waves to Quasiperiodic Motion.- 6.5. Modulated Waves in Circular Domains.- 6.6. Spatial Patterns.- 6.7. Meandering of Spiral Waves.- 7. Hidden Symmetry and Genericity.- 7.1. The Faraday Experiment.- 7.2. Hidden Symmetry in PDEs.- 7.3. The Faraday Experiment Revisited.- 7.4. Mode Interactions and Higher-Dimensional Domains.- 7.5. Lapwood Convection.- 7.6. Hemispherical Domains.- 8. Heteroclinic Cycles.- 8.1. The Guckenheimer-Holmes Example.- 8.2. Heteroclinic Cycles by Group Theory.- 8.3. Pipe Systems and Bursting.- 8.4. Cycling Chaos.- 9. Symmetric Chaos.- 9.1. Admissible Subgroups.- 9.2. Invariant Measures and Ergodic Theory.- 9.3. Detectives.- 9.4. Instantaneous and Average Symmetries, and Patterns on Average.- 9.5. Synchrony of Chaotic Oscillations and Bubbling Bifurcations.- 10. Periodic Solutions of Symmetric Hamiltonian Systems.- 10.1. The Equivariant Moser-Weinstein Theorem.- 10.2. Many-Body Problems.- 10.3. Spatio-Temporal Symmetries in Hamiltonian Systems.- 10.4. Poincaré-Birkhoff Normal Form.- 10.5. Linear Stability.- 10.6. Molecular Vibrations.

Reviews

"From the reviews: ""This book was awarded the Ferran Sunyier i Balaguer Prize for 2001, and I am sure that it will be a very useful resource not only for researchers in this area but also for those who want to obtain the benefits of using this approach in applications."" --Bulletin of the American Mathematical Society (Review of hardcover edition) [The] rich collection of examples makes the book ! extremely useful for motivation and for spreading the ideas to a large Community. This [review] is far from complete and cannot reflect the authors' unique way of presenting examples, asking questions, giving answers or forming an intuition.""(MATHEMATICAL REVIEWS)"

This book was awarded the Ferran Sunyier i Balaguer Prize for 2001, and I am sure that it will be a very useful resource not only for researchers in this area but also for those who want to obtain the benefits of using this approach in applications. <p>a Bulletin of the American Mathematical Society <p> This excellent book reflects the authors' experience in [the] exploration of the role of symmetry ina ]pattern formation in nonlinear dynamics over the past fifteen years. The selection of the material, logical structure of the monograph and presentation are perfect. Numerous historical comments, carefully selected examples accompanied [by] helpful diagrams, graphs and illustrations, valuable bibliographic references combined with panoramic introductory pieces opening each chapter, and rigorous mathematical exposition make this text enjoyable reading for everyone interested in the role played by symmetries in nonlinear dynamics and equivariant bifurcation theory. Furthermore, the book can serve as a superb sample of mathematical writing. <p>a Zentralblatt Math <p> The title gives the program of this nice book: the world seen from the symmetry point of view. In the past years we have seen a great number of papers explaining experiments and other observations in science using bifurcation and dynamical systems theory in the context of symmetry breaking. The authors of this book have shaped this developmenta ]. The theory which is presenteda ]is illustrated by many diagrams and figuresa ]. Of course in this book the authors cannot give complete proofs of all relevant statements. But this reflects the spirit of the book, which is to provide experiments, describe examples and give(some) explanations of a part of modern mathematics following one central theme: symmetrya ]. <p>[The] rich collection of examples makes the booka ]extremely useful for motivation and for spreading the ideas to a large community. This [review] is far from complete and cannot reflect the authors' unique way of presenting examples, asking questions, giving answers or forming an intuition. <p>a Mathematical Reviews

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