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

Jaume Llibre; Claùdia Valls

doi:https://doi.org/10.1017/S0308210515000906

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

Jaume Llibre, Claùdia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

© 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.

Original language	English
Pages (from-to)	1195-1210
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	146
Issue number	6
DOIs	https://doi.org/10.1017/S0308210515000906
Publication status	Published - 1 Dec 2016

Keywords

Darboux polynomial
Liouvillian first integral
Liénard polynomial differential system
exponential factor
invariant algebraic curve

Access to Document

https://doi.org/10.1017/S0308210515000906

ddd.uab.cat Link

Fingerprint Dive into the research topics of 'Liouvillian first integrals for a class of generalized Liénard polynomial differential systems'. Together they form a unique fingerprint.

Cite this

@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 = "https://doi.org/10.1017/S0308210515000906",

language = "English",

volume = "146",

pages = "1195--1210",

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

issn = "0308-2105",

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

U2 - https://doi.org/10.1017/S0308210515000906

DO - https://doi.org/10.1017/S0308210515000906

M3 - Article

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

SN - 0308-2105

IS - 6

ER -