Algebraic approach to the classification of centers in trigonometric Cherkas systems

Valls, Claudia

doi:10.1090/proc/14285

Algebraic approach to the classification of centers in trigonometric Cherkas systems
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Proc. Amer. Math. Soc. 147 (2019), 2863-2875 Request permission

Abstract:

We give a complete algebraic characterization of the non-degenerated centers for planar trigonometric Cherkas systems. The main tools used in our proof are the classical results of Cherkas on planar analytic Liénard systems, the characterization of some subfields of the quotient field of the ring of trigonometric polynomials, and results due to Rosenlicht concerning algebraic solutions to transcendental equations. The results obtained are reminiscent of the ones for planar polynomial Cherkas systems, but the proofs are different.

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