A simple solution of some composition conjectures for Abel equations

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(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Gasull, Armengol

(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mañosas Capellades, Francesc

(Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Títol variant:	The solution of the composition conjecture for Abel equations
Data:	2013
Resum:	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.
Ajuts:	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
Nota:	El títol de la versió pre-print de l'article és: The solution of the composition conjecture for Abel equations
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Periodic orbits ; Centers ; Trigonometric Abel equation ; Generalized moments ; Strongly persistent centers ; Composition Conjecture
Publicat a:	Journal of mathematical analysis and applications, Vol. 398 Núm. 2 (2013) , p. 477-486, ISSN 1096-0813

Postprint
15 p, 330.4 KB

Registre creat el 2016-05-06, darrera modificació el 2022-05-24