2026-04-14T07:49:30Zhttps://recercat.cat/oai/request

oai:recercat.cat:10459.1/629792024-12-05T21:32:50Zcom_2072_3622col_2072_479130

Center problem for trigonometric Liénard systems Gasull, Armengol Giné, Jaume Valls, Claudia Center problem Trigonometric Liénard equation Trigonometric polynomial 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. The first author is partially supported by the MINECO MTM2013-40998-P and the AGAUR (Generalitat de Catalunya) 2014SGR568 grants. The second author is partially supported by the MINECO/FEDER grant number MTM2014-53703-P and the AGAUR grant number 2014SGR 1204. The third author is partially supported by FCT/Portugal through UID/MAT/04459/2013. 2018-04-04T12:52:57Z 2019-10-05T22:18:35Z 2017 2018-04-04T12:52:58Z info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion https://doi.org/10.1016/j.jde.2017.05.008 0022-0396 http://hdl.handle.net/10459.1/62979 http://hdl.handle.net/10459.1/62979 eng MINECO/PN2013-2016/MTM2013-40998-P MINECO/PN2013-2016/MTM2014-53703-P Versió postprint del document publicat a https://doi.org/10.1016/j.jde.2017.05.008 Journal of Differential Equations, 2017, vol. 263, p. 3928-3942 cc-by-nc-nd (c) Elsevier, 2017 info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier