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Algebraic approach to the classification of centers in trigonometric Cherkas systems


Author: Claudia Valls
Journal: Proc. Amer. Math. Soc. 147 (2019), 2863-2875
MSC (2010): Primary 34C25; Secondary 37C10, 37C27
DOI: https://doi.org/10.1090/proc/14285
Published electronically: March 15, 2019
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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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Additional Information

Claudia Valls
Affiliation: Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1049–001, Lisboa, Portugal
Email: cvalls@math.ist.utl.pt

DOI: https://doi.org/10.1090/proc/14285
Keywords: Center problem, trigonometric Cherkas equation, trigonometric polynomial, algebraic solutions to transcendental equations
Received by editor(s): October 24, 2017
Received by editor(s) in revised form: April 13, 2018
Published electronically: March 15, 2019
Additional Notes: The author was partially supported by FCT/Portugal through UID/MAT/04459/2013.
Communicated by: Wenxian Shen
Article copyright: © Copyright 2019 American Mathematical Society