The generalized Liénard polynomial differential systems x'=y, y'=-g(x)-f(x)y with degg=degf+1 are not Liouvillian integrable

Jaume Llibre; Clàudia Valls

doi:https://doi.org/10.1016/j.bulsci.2014.08.010

The generalized Liénard polynomial differential systems x^'=y, y^'=-g(x)-f(x)y with degg=degf+1 are not Liouvillian integrable

Jaume Llibre, Clàudia Valls

Department of Mathematics

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

6 Citations (Scopus)

Abstract

© 2014 Elsevier Masson SAS. We prove the nonexistence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x'=y, y'=-g(x)-f(x)y, where g(x) and f(x) are arbitrary polynomials such that degg=degf+1.

Original language	English
Pages (from-to)	214-227
Journal	Bulletin des Sciences Mathematiques
Volume	139
Issue number	2
DOIs	https://doi.org/10.1016/j.bulsci.2014.08.010
Publication status	Published - 1 Jan 2015

Keywords

Darboux polynomials
Exponential factors
Liouvillian first integrals
Liénard polynomial differential systems

Access to Document

https://doi.org/10.1016/j.bulsci.2014.08.010

https://ddd.uab.cat/record/145352

Cite this

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title = "The generalized Li{\'e}nard polynomial differential systems x'=y, y'=-g(x)-f(x)y with degg=degf+1 are not Liouvillian integrable",

abstract = "{\textcopyright} 2014 Elsevier Masson SAS. We prove the nonexistence 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 g(x) and f(x) are arbitrary polynomials such that degg=degf+1.",

keywords = "Darboux polynomials, Exponential factors, Liouvillian first integrals, Li{\'e}nard polynomial differential systems",

author = "Jaume Llibre and Cl{\`a}udia Valls",

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T1 - The generalized Liénard polynomial differential systems x'=y, y'=-g(x)-f(x)y with degg=degf+1 are not Liouvillian integrable

AU - Llibre, Jaume

AU - Valls, Clàudia

PY - 2015/1/1

Y1 - 2015/1/1

N2 - © 2014 Elsevier Masson SAS. We prove the nonexistence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x'=y, y'=-g(x)-f(x)y, where g(x) and f(x) are arbitrary polynomials such that degg=degf+1.

AB - © 2014 Elsevier Masson SAS. We prove the nonexistence of Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x'=y, y'=-g(x)-f(x)y, where g(x) and f(x) are arbitrary polynomials such that degg=degf+1.

KW - Darboux polynomials

KW - Exponential factors

KW - Liouvillian first integrals

KW - Liénard polynomial differential systems

U2 - https://doi.org/10.1016/j.bulsci.2014.08.010

DO - https://doi.org/10.1016/j.bulsci.2014.08.010

M3 - Article

SN - 0007-4497

VL - 139

SP - 214

EP - 227

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

IS - 2