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Página principal > Artículos > Artículos publicados > Center problem for systems with two monomial nonlinearities |
Fecha: | 2016 |
Resumen: | We study the center problem for planar systems with a linear center at the origin that in complex coordinates have a nonlinearity formed by the sum of two monomials. Our first result lists several centers inside this family. To the best of our knowledge this list includes a new class of Darboux centers that are also persistent centers. The rest of the paper is dedicated to try to prove that the given list is exhaustive. We get several partial results that seem to indicate that this is the case. In particular, we solve the question for several general families with arbitrary high degree and for all cases of degree less or equal than 19. As a byproduct of our study we also obtain the highest known order for weak-foci of planar polynomial systems of some given degrees. |
Ayudas: | Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2011-22877 Ministerio de Economía y Competitividad UNAB10-4E-378 Ministerio de Economía y Competitividad UNAB13-4E-1604 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-1204 |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | Darboux center ; Holomorphic center ; Nondegenerate center ; Persistent center ; Poincaré-Lyapunov constants ; Reversible center |
Publicado en: | Communications on pure & applied analysis, Vol. 15 Núm. 2 (2016) , p. 577-598, ISSN 1553-5258 |
Postprint 20 p, 414.4 KB |