guest ::
| Home > Articles > Published articles > A simple solution of some composition conjectures for Abel equations |
| Home > Articles > Published articles > A simple solution of some composition conjectures for Abel equations |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universitat Autònoma de Barcelona. Departament de Matemàtiques)| Additional title: | The solution of the composition conjecture for Abel equations |
| Date: | 2013 |
| Abstract: | Trigonometric Abel differential equations appear when one studies the number of limit cycles and the center-focus problem for certain families of planar polynomial systems. Inside trigonometric Abel equations there is a class of centers, the composition centers, that have been widely studied during these last years. We fully characterize this type of centers. They are given by the couples of trigonometric polynomials for which all the generalized moments vanish and also coincide with the strongly persistent centers. This result solves the so called Composition Conjecture for trigonometric Abel differential equations. We also prove the equivalent version of this result for Abel equations with polynomial coefficients. |
| Grants: | Ministerio de Ciencia y Tecnología MTM2008-03437 Ministerio de Ciencia y Tecnología MTM2008-01486 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
| Note: | El títol de la versió pre-print de l'article és: The solution of the composition conjecture for Abel equations |
| Rights: | Tots els drets reservats.  |
| Language: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Subject: | Periodic orbits ; Centers ; Trigonometric Abel equation ; Generalized moments ; Strongly persistent centers ; Composition Conjecture |
| Published in: | Journal of mathematical analysis and applications, Vol. 398 Núm. 2 (2013) , p. 477-486, ISSN 1096-0813 |
15 p, 330.4 KB |
