Finiteness Theorems for Limit Cycles - Rilegato

Il'Yashenko, Yu. S.

Rilegato

ISBN 10: 0821845535 ISBN 13: 9780821845530

Casa editrice: Amer Mathematical Society, 1991

Riassunto

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 the results in the local theory and theorems on resolution of singularities).

Su questo libro

Contenuti:

Decomposition of a monodromy transformation into terms with noncomparable rates of decrease; Function-theoretic properties of regular functional cochains; The Phragmen-Lindelof theorem of regular functional cochains; Superexact asymptotic series; Ordering of functional cochains on a complex domain.

Su questa edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 1991
• ISBN 10: 0821845535
• ISBN 13: 9780821845530
• Rilegatura: Copertina rigida
• Numero di pagine: 288