Center problem for trigonometric Lienard systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Gasull, Armengol¹  Gine, Jaume²  Valls, Claudia³ 

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

[2] Univ Lleida, Inspires Res Ctr, Dept Matemat, Avda Jaume 2,69, Lleida 25001, Catalonia, Spain

[3] Univ Lisbon, Inst Super Tecn, Dept Matemat, Av Rovisco Pais, P-1049001 Lisbon, Portugal

关键词: Center problem;    Trigonometric Lienard equation;    Trigonometric polynomial;   

DOI  :  10.1016/j.jde.2017.05.008

来源: Elsevier

【 摘 要 】

We give a complete algebraic characterization of the non-degenerated centers for planar trigonometric Lienard systems. The main tools used in our proof are the classical results of Cherkas on planar analytic Lienard systems and the characterization of some subfields of the quotient field of the ring of trigonometric polynomials. Our results are also applied to some particular subfamilies of planar trigonometric Lienard systems. The results obtained are reminiscent of the ones for planar polynomial Lienard systems but the proofs are different. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free