The criticality of centers of potential systems at the outer boundary
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:	2016
Abstract:	The number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied. We call this number the criticality at the outer boundary. Our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1. We apply them to study the bifurcation diagram of the period function of X = −y∂ x ((x 1) p − (x 1) q )∂ y with q < p. This family was previously studied for q = 1 by Y. Miyamoto and K. Yagasaki.
Grants:	Ministerio de Educación y Ciencia MTM2014-52209-C2-P
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Bifurcation ; Center ; Critical periodic orbit ; Criticality ; Period function
Published in:	Journal of differential equations, Vol. 260 (2016) , p. 4918-4972, ISSN 1090-2732

DOI: 10.1016/j.jde.2015.11.040

Postprint 41 p, 612.7 KB

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