Finiteness Theorems for Limit Cycles (Translations of Mathematical Monographs)
Language: English
Published by American Mathematical Society, 1991
- Hardcover
- New

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In English.
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- Title
- Finiteness Theorems for Limit Cycles (Translations of Mathematical Monographs)
- Author
- Yu. S. Ilyashenko
- Publisher
- American Mathematical Society
- Publication year
- 1991
- Condition
- New
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 0821845535
- ISBN 13
- 9780821845530
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).
"Synopsis" may belong to another edition of this title.
Language Notes
Text: English (translation)
Original Language: Russian
Original Language: Russian
"About the title" may belong to another edition of this title.
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