Asymptotic expansion of the period function.
type: Item
instance of: scholarly article
title: Asymptotic expansion of the period function.
zbMATH Open document ID: 1048.34084
DOI: 10.1016/S0022-0396(03)00091-3
author: M. Saavedra
published in: Journal of Differential Equations
publication date: 2003-11-10T00:00:00Z
review text: Let \(P\) be a polycycle (i.e., a connected union of singularities and joining them integral curves) of an analytic vector field in the plane. The author studies the return-time function \(T\) near \(P\). Conditions are given under which the asymptotic expansions of the function \(T\) and its derivative \(T'\) converge to these functions absolutely and uniformly. The results are applied, for example, to analytic vector fields having a Darboux integral and to systems with nilpotent centers and foci.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 2002184
zbMATH Keywords: polycycle
zbMATH Keywords: return-time function
reviewed by: Sergei Yu. Pilyugin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2002184