Centre and isochronicity conditions for systems with homogeneous nonlinearities

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Títol:	Centre and isochronicity conditions for systems with homogeneous nonlinearities
Autor/a:	Gasull Embid, Armengol; Guillamon Grabolosa, Antoni; Mañosa Fernández, Víctor
Altres autors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
Abstract:	We study the centre-focus problem for systems with homogeneous nonlinearities. In the centre case we study the characterization of the isochronous centres. More explicitly, we derive six necessary conditions to be a centre and six necessary conditions to be an isochronous centre. These conditions are expressed in complex notation and are suitable to be utilized in any computer algebra system. By using this approach we get the necessary and sufficient conditions to be a centre or an isochronous centre for a general system with homogeneous nonlinearities of degree two or three. This last result is already known but we give a slightly different proof.
Matèries:	-Differential equations -Global analysis (Mathematics) -Homogeneous Nonlinearities -Equacions diferencials ordinàries -Varietats (Matemàtica) -Classificació AMS::34 Ordinary differential equations::34C Qualitative theory -Classificació AMS::58 Global analysis, analysis on manifolds
Drets:	Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Tipus de document:	Article
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