Integrability conditions of a resonant saddle in generalized Liénard-like complex polynomial differential systems

Jaume Giné; Jaume Llibre

doi:10.1016/j.chaos.2017.01.014

Integrability conditions of a resonant saddle in generalized Liénard-like complex polynomial differential systems

Jaume Giné, Jaume Llibre

Department of Mathematics

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

5 Citations (Scopus)

Abstract

© 2017 We consider a complex differential system with a resonant saddle at the origin. We compute the resonant saddle quantities and using Gröbner bases we find the integrability conditions for such systems up to a certain degree. We also establish a conjecture about the integrability conditions for such systems when they have arbitrary degree.

Original language	English
Pages (from-to)	130-131
Journal	Chaos, Solitons and Fractals
Volume	96
DOIs	https://doi.org/10.1016/j.chaos.2017.01.014
Publication status	Published - 1 Mar 2017

Keywords

Analytic integrability
Center problem
Polynomial complex differential systems

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10.1016/j.chaos.2017.01.014

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title = "Integrability conditions of a resonant saddle in generalized Li{\'e}nard-like complex polynomial differential systems",

abstract = "{\textcopyright} 2017 We consider a complex differential system with a resonant saddle at the origin. We compute the resonant saddle quantities and using Gr{\"o}bner bases we find the integrability conditions for such systems up to a certain degree. We also establish a conjecture about the integrability conditions for such systems when they have arbitrary degree.",

keywords = "Analytic integrability, Center problem, Polynomial complex differential systems",

author = "Jaume Gin{\'e} and Jaume Llibre",

year = "2017",

month = mar,

day = "1",

doi = "10.1016/j.chaos.2017.01.014",

language = "English",

volume = "96",

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journal = "Chaos, Solitons and Fractals",

issn = "0960-0779",

publisher = "Elsevier Limited",

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TY - JOUR

T1 - Integrability conditions of a resonant saddle in generalized Liénard-like complex polynomial differential systems

AU - Giné, Jaume

AU - Llibre, Jaume

PY - 2017/3/1

Y1 - 2017/3/1

N2 - © 2017 We consider a complex differential system with a resonant saddle at the origin. We compute the resonant saddle quantities and using Gröbner bases we find the integrability conditions for such systems up to a certain degree. We also establish a conjecture about the integrability conditions for such systems when they have arbitrary degree.

AB - © 2017 We consider a complex differential system with a resonant saddle at the origin. We compute the resonant saddle quantities and using Gröbner bases we find the integrability conditions for such systems up to a certain degree. We also establish a conjecture about the integrability conditions for such systems when they have arbitrary degree.

KW - Analytic integrability

KW - Center problem

KW - Polynomial complex differential systems

U2 - 10.1016/j.chaos.2017.01.014

DO - 10.1016/j.chaos.2017.01.014

M3 - Article

VL - 96

SP - 130

EP - 131

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

ER -