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A simple solution of some composition conjectures for Abel equations
Cima, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Periodic orbits ; Centers ; Trigonometric Abel equation ; Generalized moments ; Strongly persistent centers ; Composition Conjecture
Publicat a: Journal of Mathematical Analysis and Applications 4x 0022-247X, Vol. 398 Núm. 2 (2013) , p. 477-486

DOI: 10.1016/j.jmaa.2012.09.006

15 p, 330.4 KB

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