Asymptotic expansion of the period function II

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:222

Article

Saavedra, M

关键词: vector field;    polycycle;    desingularization;    period function;    asymptotic expansion;   

DOI  :  10.1016/j.jde.2005.04.011

来源: Elsevier

【 摘 要 】

Let P be a not necessarily bounded polycycle of an analytic vector field on an open set of the plane. Suppose that the singularities which appear after desingularization of the vertices of P are hyperbolic. Consider the function T defined by the return time near P. It is shown that the function T and its derivative T' have asymptotic expansions similar to the series of Dulac but with negative powers. (c) 2005 Published by Elsevier Inc.

【 授权许可】

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