Memoirs of the American Mathematical Society 2003; 86 pp; softcover Volume: 165 ISBN10: 0821833731 ISBN13: 9780821833735 List Price: US$57 Individual Members: US$34.20 Institutional Members: US$45.60 Order Code: MEMO/165/786
 In this paper, bifurcations of stationary and timeperiodic solutions to reactiondiffusion systems are studied. We develop a centermanifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns. In particular, we show the existence of localized pulses near saddlenodes, critical Gibbs kernels in the cusp, focus patterns in Turing instabilities, and active or passive target patterns in oscillatory instabilities. Readership Graduate students and research mathematicians interested in differential equations. Table of Contents  Introduction
 Instabilities in one space dimension
 Stationary radially symmetric patterns
 Timeperiodic radially symmetric patterns
 Discussion
 Bibliography
