TY  - BOOK
AU  - Fiedler,Bernold
ED  - SpringerLink (Online service)
TI  - Global Bifurcation of Periodic Solutions with Symmetry
T2  - Lecture Notes in Mathematics,
SN  - 9783540391500
AV  - QA299.6-433 
U1  - 515 23
PY  - 1988///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Global analysis (Mathematics)
KW  - Mathematical physics
KW  - Analysis
KW  - Mathematical and Computational Physics
N1  - Main results -- No symmetry — a survey -- Virtual symmetry -- Generic local theory -- Generic global theory -- General global theory -- Applications -- Discussion -- Appendix on genericity
N2  - This largely self-contained research monograph addresses the following type of questions. Suppose one encounters a continuous time dynamical system with some built-in symmetry. Should one expect periodic motions which somehow reflect this symmetry? And how would periodicity harmonize with symmetry? Probing into these questions leads from dynamics to topology, algebra, singularity theory, and to many applications. Within a global approach, the emphasis is on periodic motions far from equilibrium. Mathematical methods include bifurcation theory, transversality theory, and generic approximations. A new homotopy invariant is designed to study the global interdependence of symmetric periodic motions. Besides mathematical techniques, the book contains 5 largely nontechnical chapters. The first three outline the main questions, results and methods. A detailed discussion pursues theoretical consequences and open problems. Results are illustrated by a variety of applications including coupled oscillators and rotating waves: these links to such disciplines as theoretical biology, chemistry, fluid dynamics, physics and their engineering counterparts make the book directly accessible to a wider audience
UR  - http://dx.doi.org/10.1007/BFb0082943
ER  -