Center problem for trigonometric Liénard systems

Armengol Gasull; Jaume Giné; Claudia Valls

doi:10.1016/j.jde.2017.05.008

Center problem for trigonometric Liénard systems

Armengol Gasull, Jaume Giné, Claudia Valls

Departament de Matemàtiques

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Resum

© 2017 Elsevier Inc. 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.

Idioma original	Anglès
Pàgines (de-a)	3928-3942
Revista	Journal of Differential Equations
Volum	263
Número	7
DOIs	https://doi.org/10.1016/j.jde.2017.05.008
Estat de la publicació	Publicada - 5 d’oct. 2017

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10.1016/j.jde.2017.05.008

https://ddd.uab.cat/record/182524

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@article{2004d798bf28489ca70dc7ade92a0131,

title = "Center problem for trigonometric Li{\'e}nard systems",

abstract = "{\textcopyright} 2017 Elsevier Inc. We give a complete algebraic characterization of the non-degenerated centers for planar trigonometric Li{\'e}nard systems. The main tools used in our proof are the classical results of Cherkas on planar analytic Li{\'e}nard 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 Li{\'e}nard systems. The results obtained are reminiscent of the ones for planar polynomial Li{\'e}nard systems but the proofs are different.",

keywords = "Center problem, Trigonometric Li{\'e}nard equation, Trigonometric polynomial",

author = "Armengol Gasull and Jaume Gin{\'e} and Claudia Valls",

year = "2017",

month = oct,

day = "5",

doi = "10.1016/j.jde.2017.05.008",

language = "English",

volume = "263",

pages = "3928--3942",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "7",

}

TY - JOUR

T1 - Center problem for trigonometric Liénard systems

AU - Gasull, Armengol

AU - Giné, Jaume

AU - Valls, Claudia

PY - 2017/10/5

Y1 - 2017/10/5

N2 - © 2017 Elsevier Inc. 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.

AB - © 2017 Elsevier Inc. 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.

KW - Center problem

KW - Trigonometric Liénard equation

KW - Trigonometric polynomial

U2 - 10.1016/j.jde.2017.05.008

DO - 10.1016/j.jde.2017.05.008

M3 - Article

SN - 0022-0396

VL - 263

SP - 3928

EP - 3942

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 7

ER -

Center problem for trigonometric Liénard systems

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