About the Book
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001.
The framework of a ~symmetrya (TM) 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. Ita (TM)s exposition is organized around a wide variety of applications ranging from theoretical physics to evolutionary biology.
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.