A simple solution of some composition conjectures for Abel equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:398

Article

Cima, Anna¹  Gasull, Armengol¹  Manosas, Francesc¹ 

[1] Univ Autonoma Barcelona, Fac Ciencies, Dept Matemat, E-08193 Barcelona, Spain

关键词: Periodic orbits;    Centers;    Trigonometric Abel equation;    Generalized moments;    Strongly persistent centers;    Composition conjecture;   

DOI  :  10.1016/j.jmaa.2012.09.006

来源: Elsevier

【 摘 要 】

Trigonometric Abel differential equations appear in the study of the number of limit cycles and the center-focus problem for certain families of planar polynomial systems. The composition centers are a class of centers for trigonometric Abel equations which have been widely studied during last years. We characterize this type of centers as the ones given by couples of trigonometric polynomials for which all the generalized moments vanish. They also coincide with the strongly and the highly persistent centers. Our result gives a simple and self-contained proof of the so called Composition Conjecture for trigonometric Abel differential equations. We also prove a similar version of this result for Abel equations with polynomial coefficients. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free