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Pàgina inicial > Articles > Articles publicats > Analytic tools to bound the criticality at the outer boundary of the period annulus |
Data: | 2018 |
Resum: | 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. |
Ajuts: | Ministerio de Economía y Competitividad MTM2014-52209-C2-1-P Agència de Gestió d'Ajuts Universitaris i de Recerca FI/DGR2014 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Bifurcation ; Center ; Chebyshev system ; Critical periodic orbit ; Criticality ; Period function |
Publicat a: | Journal of dynamics and differential equations, Vol. 30, issue 3 (Sep. 2018) , p. 883-909, ISSN 1572-9222 |
Postprint 23 p, 533.7 KB |