2006, Volume 254

This volume contains papers of participants of the seminar on dynamical systems that is regularly held at the Faculty of Mechanics and Mathematics, Moscow State University. For more than 30 years, Yu. S. Il'yashenko has been either the chairman or a co-chairman of this seminar. Many authors of the present volume are participants of the seminar of the Department of Ordinary Differential Equations, Steklov Institute of Mathematics; in recent years, this seminar has been headed by D. V. Anosov, A. A. Bolibrukh, and Yu. S. Il'yashenko. The volume addresses various questions in the theory of analytic differential equations in real and complex domains. The main result of this volume is a fundamental theorem by N. B. Medvedeva on the analytic solvability of the problem of distinguishing between a center and a focus. This theorem completes more than 100 years of research initiated by H. Poincaré. Other articles are devoted to the global theory of polynomial and analytic foliations in the complex plane, theory of normal forms, zeros of Abelian integrals, upper bounds for the number of limit cycles for special classes of polynomial vector fields, and upper bounds for the number of topological types (modulo limit cycles) for polynomial vector fields of fixed degree.
The volume is addressed to scientists, postgraduates, and students who specialize in the theory of differential equations and in complex analysis.

ISBN: 5-02-034087-1