Finiteness Theorems for Limit Cycles (Translations of Mathematical Monographs) - Hardcover

Yu. S. Ilyashenko

Hardcover

ISBN 10: 0821845535 ISBN 13: 9780821845530

Publisher: American Mathematical Society, 1991

Synopsis

This book is devoted to the following finiteness theorem: A polynomial vector field on the real plane has a finite number of limit cycles. To prove the theorem, it suffices to note that limit cycles cannot accumulate on a polycycle of an analytic vector field. This approach necessitates investigation of the monodromy transformation (also known as the Poincare return mapping or the first return mapping) corresponding to this cycle. To carry out this investigation, this book utilizes five sources: The theory of Dulac, use of the complex domain, resolution of singularities, the geometric theory of normal forms, and superexact asymptotic series. In the introduction, the author presents results about this problem that were known up to the writing of the present book, with full proofs (except in the case of results in the local theory and theorems on resolution of singularities).

About this title

Language Notes

Text: English (translation)
Original Language: Russian

Review

The viewpoint is high and the techniques are delicate and profound. --Zentralblatt für Mathematik

Edition details

• Publisher: American Mathematical Society
• Publication date: 1991
• Language: English
• ISBN 10: 0821845535
• ISBN 13: 9780821845530
• Binding: Hardcover
• Number of pages: 288