Transitions of Mathematical Monographs Vol. 94. ix, 288 p. 26 cm. Ex library wth labels on spine and rear pastedown, ink stamp on rear endpaper, top edge.

Bestandsnummer des Verk�ufers 146840

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Bibliografische Details

Titel

Finiteness Theorems for Limit Cycles

Verlag

American Mathematical Society, Providence, RI

Erscheinungsjahr

1991

Sprache

Englisch

ISBN-10

0821845535

ISBN-13

9780821845530

Einband

Hardcover

Zustand

ex library-good

Verk�uferkataloge

Science

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Inhaltsangabe

Can we be absolutely sure that a polynomial vector field on the real plane has a finite number of limit cycles? Yes, one proof involves the theory of Dulac, going out into the complex domain, the resolution of singularities, the geometric theory of normal forms, and the superexact asymptotic series. No index. Translated from the Russian. Annotation copyright Book News, Inc. Portland, Or.

Rese�a del editor

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).

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