Center problem for trigonometric Liénard systems

Gasull, Armengol; Giné, Jaume; Valls, Claudia

doi:https://doi.org/10.1016/j.jde.2017.05.008

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Issue date

2017

Author

Gasull, Armengol

Giné, Jaume

Valls, Claudia

Abstract

We give a complete algebraic characterization of the non-degenerated centers for planar trigonometric Liénard systems. The main tools used in our proof are the classical results of Cherkas on planar analytic Liénard 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 Liénard systems. The results obtained are reminiscent of the ones for planar polynomial Liénard systems but the proofs are different.