Averaging methods for finding periodic orbits via Brouwer degree.
type: Item
instance of: scholarly article
title: Averaging methods for finding periodic orbits via Brouwer degree.
zbMATH Open document ID: 1055.34086
author: Adriana Buică
author: Jaume Llibre
published in: Bulletin des Sciences Mathématiques
publication date: 2004-03-14T00:00:00Z
review text: The authors consider the problem of finding periodic solutions for a differential system whose right-hand side depends on a small parameter. Taking into account that the problem of finding periodic solutions for some differential systems is equivalent to that of finding zeros of some corresponding operator equations, they obtain different results by using the averaging method in combination with topological methods based on Brouwer degree theory and coincidence degree theory. Here, the main contribution to the averaging theory is the dropping of regularity conditions (up to second order in the parameter). Moreover, a result for the third-order averaging method is given. Finally, the authors provide a way to study bifurcations of limit cycles from the period annulus of a planar system and notice relations with the displacement function.
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 47H11
zbMATH DE Number: 2056358
zbMATH Keywords: averaging method
zbMATH Keywords: periodic solutions
zbMATH Keywords: Brouwer degree
zbMATH Keywords: coincidence degree
zbMATH Keywords: limit cycles
zbMATH Keywords: bifurcation
reviewed by: Antonio Cañada
MaRDI profile type: Publication
full work available at URL: j.bulsci.2003.09.002
OpenAlex ID: W2158334808
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DOI: 10.1016/J.BULSCI.2003.09.002
description: scientific article; zbMATH DE number 2056358