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Algebraic and analytical tools for the study of the period function
Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)

Date: 2014
Abstract: In this paper we consider analytic planar differential systems having a first integral of the form H(x, y) = A(x) + B(x)y + C(x)y2 and an integrating factor κ(x) not depending on y. Our aim is to provide tools to study the period function of the centers of this type of differential system and to this end we prove three results. Theorem A gives a characterization of isochronicity, a criterion to bound the number of critical periods and a necessary condition for the period function to be monotone. Theorem B is intended for being applied in combination with Theorem A in an algebraic setting that we shall specify. Finally, Theorem C is devoted to study the number of critical periods bifurcating from the period annulus of an isochrone perturbed linearly inside a family of centers. Four different applications are given to illustrate these results.
Grants: Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792
Ministerio de Ciencia e Innovación MTM-2011-C02-02
Ministerio de Ciencia e Innovación MTM-2008-034
Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Rights: Tots els drets reservats.
Language: Anglès
Document: Article ; recerca ; Versió acceptada per publicar
Subject: Bifurcations ; Center ; Critical period ; Period function
Published in: Journal of differential equations, Vol. 254 (2014) , p. 2464-2484, ISSN 1090-2732

DOI: 10.1016/j.jde.2014.05.044


Postprint
18 p, 451.0 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2016-05-06, last modified 2023-10-01



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