Memoirs of the American Mathematical Society 1992; 179 pp; softcover Volume: 100 ISBN10: 0821825429 ISBN13: 9780821825426 List Price: US$36 Individual Members: US$21.60 Institutional Members: US$28.80 Order Code: MEMO/100/481
 This work is devoted to a detailed study of the equivariant degree and its applications for the case of an \(S^1\)action. This degree is an element of the equivariant homotopy group of spheres, which are computed in a stepbystep extension process. Applications include the index of an isolated orbit, branching and Hopf bifurcation, and period doubling and symmetry breaking for systems of autonomous differential equations. The authors have paid special attention to making the text as selfcontained as possible, so that the only background required is some familiarity with the basic ideas of homotopy theory and of Floquet theory in differential equations. Illustrating in a natural way the interplay between topology and analysis, this book will be of interest to researchers and graduate students. Readership Researchers and graduate students who wish to learn about the interplay between topology and analysis. Table of Contents  Preliminaries
 Extensions of \(S^1\)maps
 Homotopy groups of \(S^1\)maps
 Degree of \(S^1\)maps
 \(S^1\)index of an isolated nonstationary orbit and applications
 Index of an isolated orbit of stationary solutions and applications
 Virtual periods and orbit index
 Appendix: Additivity up to one suspension
