
2006, Volume 254




Nonlinear analytic differential equations
Collected papers
Volume Editor: Yu. S. Ilyashenko^{} Editor in Chief: E. F. Mishchenko^{}
Abstract: 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 cochairman 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: 5020340871
Full text:
Contents
Citation:
Nonlinear analytic differential equations, Collected papers, Trudy Mat. Inst. Steklova, 254, ed. Yu. S. Ilyashenko, E. F. Mishchenko, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 271 pp.
Citation in format AMSBIB:
\Bibitem{1}
\book Nonlinear analytic differential equations
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2006
\vol 254
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\ed Yu.~S.~Ilyashenko, E.~F.~Mishchenko
\totalpages 271
\mathnet{http://mi.mathnet.ru/book267}
Linking options:
http://mi.mathnet.ru/eng/book267
Additional information
Nonlinear Analytic Differential Equations
Collected papers
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 cochairman 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. Poincare. 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. 

