On the analytic integrability of the lienard analytic differential systems

Jaume Llibre; Claudia Valls

doi:10.3934/dcdsb.2016.21.557

On the analytic integrability of the lienard analytic differential systems

Jaume Llibre, Claudia Valls

Departament de Matemàtiques

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10 Cites (Scopus)

Resum

We consider the Lienard analytic differential systems x = y, y =-g(x)-f(x)y, where f, g: R → R are analytic functions and the origin is an isolated singular point. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the origin and the existence of global analytic first integrals.

Idioma original	Anglès
Pàgines (de-a)	557-573
Revista	Discrete and Continuous Dynamical Systems - Series B
Volum	21
Número	2
DOIs	https://doi.org/10.3934/dcdsb.2016.21.557
Estat de la publicació	Publicada - 1 de març 2016

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10.3934/dcdsb.2016.21.557

https://ddd.uab.cat/record/169480

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title = "On the analytic integrability of the lienard analytic differential systems",

abstract = "We consider the Lienard analytic differential systems x = y, y =-g(x)-f(x)y, where f, g: R → R are analytic functions and the origin is an isolated singular point. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the origin and the existence of global analytic first integrals.",

keywords = "Analytic integrability, Formal integrability, Lienard system",

author = "Jaume Llibre and Claudia Valls",

year = "2016",

month = mar,

day = "1",

doi = "10.3934/dcdsb.2016.21.557",

language = "English",

volume = "21",

pages = "557--573",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "American Institute of Mathematical Sciences",

number = "2",

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TY - JOUR

T1 - On the analytic integrability of the lienard analytic differential systems

AU - Llibre, Jaume

AU - Valls, Claudia

PY - 2016/3/1

Y1 - 2016/3/1

N2 - We consider the Lienard analytic differential systems x = y, y =-g(x)-f(x)y, where f, g: R → R are analytic functions and the origin is an isolated singular point. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the origin and the existence of global analytic first integrals.

AB - We consider the Lienard analytic differential systems x = y, y =-g(x)-f(x)y, where f, g: R → R are analytic functions and the origin is an isolated singular point. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the origin and the existence of global analytic first integrals.

KW - Analytic integrability

KW - Formal integrability

KW - Lienard system

U2 - 10.3934/dcdsb.2016.21.557

DO - 10.3934/dcdsb.2016.21.557

M3 - Article

SN - 1531-3492

VL - 21

SP - 557

EP - 573

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 2

ER -

On the analytic integrability of the lienard analytic differential systems

Resum

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