Liouvillian first integrals for a class of generalized Liénard polynomial differential systems

Jaume Llibre; Claùdia Valls

doi:10.1017/S0308210515000906

Liouvillian first integrals for a class of generalized Liénard polynomial differential systems

Jaume Llibre, Claùdia Valls

Departament de Matemàtiques

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Resum

© 2016 Royal Society of Edinburgh. We study the existence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x' = y, y' =-g(x)-f(x)y, where f(x) = 3Q(x)Q'(x)P(x) + Q(x)2 P'(x) and g(x) = Q(x)Q'(x)(Q(x)2 P(x)2-1) with P,Q [x]. This class of generalized Liénard polynomial differential systems has the invariant algebraic curve (y + Q(x)P(x))2-Q(x)2 = 0 of hyperelliptic type.

Idioma original	Anglès
Pàgines (de-a)	1195-1210
Revista	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volum	146
Número	6
DOIs	https://doi.org/10.1017/S0308210515000906
Estat de la publicació	Publicada - 1 de des. 2016

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10.1017/S0308210515000906

https://ddd.uab.cat/record/221044

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https://www.scopus.com/pages/publications/84978137352

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@article{2b768ec3e0e945f5bb1cd33b9a35d0af,

title = "Liouvillian first integrals for a class of generalized Li{\'e}nard polynomial differential systems",

abstract = "{\textcopyright} 2016 Royal Society of Edinburgh. We study the existence of Liouvillian first integrals for the generalized Li{\'e}nard polynomial differential systems of the form x' = y, y' =-g(x)-f(x)y, where f(x) = 3Q(x)Q'(x)P(x) + Q(x)2 P'(x) and g(x) = Q(x)Q'(x)(Q(x)2 P(x)2-1) with P,Q [x]. This class of generalized Li{\'e}nard polynomial differential systems has the invariant algebraic curve (y + Q(x)P(x))2-Q(x)2 = 0 of hyperelliptic type.",

keywords = "Darboux polynomial, Liouvillian first integral, Li{\'e}nard polynomial differential system, exponential factor, invariant algebraic curve",

author = "Jaume Llibre and Cla{\`u}dia Valls",

year = "2016",

month = dec,

day = "1",

doi = "10.1017/S0308210515000906",

language = "English",

volume = "146",

pages = "1195--1210",

journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",

issn = "0308-2105",

publisher = "Cambridge University Press",

number = "6",

}

TY - JOUR

T1 - Liouvillian first integrals for a class of generalized Liénard polynomial differential systems

AU - Llibre, Jaume

AU - Valls, Claùdia

PY - 2016/12/1

Y1 - 2016/12/1

N2 - © 2016 Royal Society of Edinburgh. We study the existence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x' = y, y' =-g(x)-f(x)y, where f(x) = 3Q(x)Q'(x)P(x) + Q(x)2 P'(x) and g(x) = Q(x)Q'(x)(Q(x)2 P(x)2-1) with P,Q [x]. This class of generalized Liénard polynomial differential systems has the invariant algebraic curve (y + Q(x)P(x))2-Q(x)2 = 0 of hyperelliptic type.

AB - © 2016 Royal Society of Edinburgh. We study the existence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x' = y, y' =-g(x)-f(x)y, where f(x) = 3Q(x)Q'(x)P(x) + Q(x)2 P'(x) and g(x) = Q(x)Q'(x)(Q(x)2 P(x)2-1) with P,Q [x]. This class of generalized Liénard polynomial differential systems has the invariant algebraic curve (y + Q(x)P(x))2-Q(x)2 = 0 of hyperelliptic type.

KW - Darboux polynomial

KW - Liouvillian first integral

KW - Liénard polynomial differential system

KW - exponential factor

KW - invariant algebraic curve

UR - https://www.scopus.com/pages/publications/84978137352

U2 - 10.1017/S0308210515000906

DO - 10.1017/S0308210515000906

M3 - Article

SN - 0308-2105

VL - 146

SP - 1195

EP - 1210

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

IS - 6

ER -

Liouvillian first integrals for a class of generalized Liénard polynomial differential systems

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