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

9 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

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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.",

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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

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EP - 261

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