Analytic tools to bound the criticality at the outer boundary of the period annulus
Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rojas, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)

Date:	2018
Abstract:	In this paper we consider planar potential differential systems and we study the bifurcation of critical periodic orbits from the outer boundary of the period annulus of a center. In the literature the usual approach to tackle this problem is to obtain a uniform asymptotic expansion of the period function near the outer boundary. The novelty in the present paper is that we directly embed the derivative of the period function into a collection of functions that form a Chebyshev system near the outer boundary. We obtain in this way explicit sufficient conditions in order that at most n 0 critical periodic orbits bifurcate from the outer boundary. These theoretical results are then applied to study the bifurcation diagram of the period function of the family ẍ= xp − xq , p, q ∈ R with p > q.
Grants:	Ministerio de Economía y Competitividad MTM2014-52209-C2-1-P Agència de Gestió d'Ajuts Universitaris i de Recerca FI/DGR2014
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Bifurcation ; Center ; Chebyshev system ; Critical periodic orbit ; Criticality ; Period function
Published in:	Journal of dynamics and differential equations, Vol. 30, issue 3 (Sep. 2018) , p. 883-909, ISSN 1572-9222

DOI: 10.1007/s10884-016-9559-x

Postprint 23 p, 533.7 KB

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