On the local analytic integrability at the singular point of a class of Liénard analytic differential systems

Jaume Llibre; Clàudia Valls

doi:10.1090/S0002-9939-09-10036-9

On the local analytic integrability at the singular point of a class of Liénard analytic differential systems

Jaume Llibre, Clàudia Valls

Department of Mathematics

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

10 Citations (Scopus)

Abstract

We consider the Liénard analytic differential systems ẋ = y, ẏ = -cx - f(x)y, with c ε ℝ and f : ℝ → ℝ an analytic function. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the singular point located at the origin. © 2009 American Mathematical Society.

Original language	English
Pages (from-to)	253-261
Journal	Proceedings of the American Mathematical Society
Volume	138
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-09-10036-9
Publication status	Published - 1 Jan 2010

Keywords

Analytic integrability
Liénard differential system
Local analytic integrability

Access to Document

10.1090/S0002-9939-09-10036-9

Cite this

@article{e58614141b694b5e817202684bc5d645,

title = "On the local analytic integrability at the singular point of a class of Li{\'e}nard analytic differential systems",

abstract = "We consider the Li{\'e}nard analytic differential systems ẋ = y, ẏ = -cx - f(x)y, with c ε ℝ and f : ℝ → ℝ an analytic function. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the singular point located at the origin. {\textcopyright} 2009 American Mathematical Society.",

keywords = "Analytic integrability, Li{\'e}nard differential system, Local analytic integrability",

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

year = "2010",

month = jan,

day = "1",

doi = "10.1090/S0002-9939-09-10036-9",

language = "English",

volume = "138",

pages = "253--261",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

number = "1",

}

TY - JOUR

T1 - On the local analytic integrability at the singular point of a class of Liénard analytic differential systems

AU - Llibre, Jaume

AU - Valls, Clàudia

PY - 2010/1/1

Y1 - 2010/1/1

N2 - We consider the Liénard analytic differential systems ẋ = y, ẏ = -cx - f(x)y, with c ε ℝ and f : ℝ → ℝ an analytic function. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the singular point located at the origin. © 2009 American Mathematical Society.

AB - We consider the Liénard analytic differential systems ẋ = y, ẏ = -cx - f(x)y, with c ε ℝ and f : ℝ → ℝ an analytic function. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the singular point located at the origin. © 2009 American Mathematical Society.

KW - Analytic integrability

KW - Liénard differential system

KW - Local analytic integrability

U2 - 10.1090/S0002-9939-09-10036-9

DO - 10.1090/S0002-9939-09-10036-9

M3 - Article

VL - 138

SP - 253

EP - 261

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -

On the local analytic integrability at the singular point of a class of Liénard analytic differential systems

Abstract

Keywords

Access to Document

Fingerprint

Cite this