American Mathematical Society TranslationsSeries 2 Advances in the Mathematical Sciences 1995; 219 pp; hardcover Volume: 165 ISBN10: 082180362X ISBN13: 9780821803622 List Price: US$116 Member Price: US$92.80 Order Code: TRANS2/165
 This book examines qualitative properties of vector fields in the plane, in the spirit of Hilbert's Sixteenth Problem. Two principal topics explored are bifurcations of limit cycles of planar vector fields and desingularization of singular points for individual vector fields and for analytic families of such fields. In addition to presenting important new developments in this area, this book contains an introductory paper which outlines the general context and describes connections between the papers in the volume. The book will appeal to researchers and graduate students working in the qualitative theory of ordinary differential equations and dynamical systems. Readership Researchers and graduate students working in the qualitative theory of ordinary differential equations. Table of Contents  Yu. Ilyashenko and S. Yakovenko  Concerning the Hilbert sixteenth problem
 Yu. Ilyashenko and S. Yakovenko  Finite cyclicity of elementary polycycles in generic families
 S. Trifonov  Desingularization in families of analytic differential equations
 O. Kleban  Order of the topologically sufficient jet of a smooth vector field on the real plane at a singular point of finite multiplicity
 A. Kotova and V. Stanzo  On fewparameter generic families of vector fields on the twodimensional sphere
 S. Yakovenko  A geometric proof of the Bautin theorem
