Synopses & Reviews
Pattern formation in physical systems is one of the major research frontiers of mathematics. A central theme of this book is that many instances of pattern formation can be understood within a single framework: symmetry. This book applies symmetry methods to increasingly complex kinds of dynamic behavior: equilibria, period-doubling, time-periodic states, homoclinic and heteroclinic orbits, and chaos. Examples are drawn from both ODEs and PDEs. In each case the type of dynamical behavior being studied is motivated through applications, drawn from a wide variety of scientific disciplines ranging from theoretical physics to evolutionary biology.
Review
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)
Review
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)
Synopsis
The framework of 'symmetry' provides an important route between the abstract theory and experimental observations, especially for the study of pattern formation in physical systems. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. It's exposition is organized around a wide variety of applications ranging from theoretical physics to evolutionary biology.
Synopsis
The framework of 'symmetry' provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications.
From the reviews:
"[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS
Table of Contents
Preface.- Steady-State Bifurcation.- Linear Stability.- Time Periodicity and Spatio-Temporal Symmetry.- Hopf Bifurcation with Symmetry.- Steady-State Bifurcations in Euclidean Equivariant Systems.- Bifurcation From Group Orbits.- Hidden Symmetry and Genericity.- Heteroclinic Cycles.- Symmetric Chaos.- Periodic Solutions of Symmetric Hamiltonian Systems.