Finiteness theorems for limit cycles

Bibliographic Information

Finiteness theorems for limit cycles

Yu.S. Ilʹyashenko

(Translations of mathematical monographs, v. 94)

American Mathematical Society, c1991

Other Title

Теоремы конечности для предельных циклов

Teoremy konechnosti dli︠a︡ predelʹnykh t︠s︡iklov

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Note

Includes bibliographical references (p. 287-288)

Translated from the Russian by H.H. McFaden

Description and Table of Contents

Description

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.

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