Memoirs of the American Mathematical Society 1998; 108 pp; softcover Volume: 134 ISBN10: 082180796X ISBN13: 9780821807965 List Price: US$49 Individual Members: US$29.40 Institutional Members: US$39.20 Order Code: MEMO/134/639
 This book solves a problem that has been open for over 20 yearsthe complete classification of structurally stable quadratic vector fields modulo limit cycles. The 1950s saw the first real impetus given to the development of the qualitative theory of quadratic vector fields, although prior and ongoing interest in the topic can be shown by the more than 800 papers that have been published on the subject. One of the problems in the qualitative theory of quadratic vector fields is the classification of all structurally stable ones: In this work the authors solve this problem completely modulo limit cycles and give all possible phase portraits for such structurally stable quadratic vector fields. Readership Research mathematicians and graduate students interested in qualitative theory of planar differential equations; physicists and engineers interested in dynamical systems. Table of Contents  Introduction
 Preliminary definitions
 Structural stability theorems
 Some preliminary tools
 Proof of Theorem 1.1(a)
 Proof of Theorem 1.1(b)
 Proofs of Theorems 1.2, 1.3 and 1.4
 Structural stability and the parameter space
 Bibliography
