Planar quasi-homogeneous polynomial differential systems and their integrability

Belén García; Jaume Llibre; Jesús S. Pérez del Río

doi:https://doi.org/10.1016/j.jde.2013.07.032

Planar quasi-homogeneous polynomial differential systems and their integrability

Belén García, Jaume Llibre, Jesús S. Pérez del Río

Department of Mathematics

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

28 Citations (Scopus)

Abstract

In this paper we study the quasi-homogeneous polynomial differential systems and provide an algorithm for obtaining all these systems with a given degree. Using this algorithm we obtain all quasi-homogeneous vector fields of degree 2 and 3.The quasi-homogeneous polynomial differential systems are Liouvillian integrable. In particular, we characterize all the quasi-homogeneous vector fields of degree 2 and 3 having a polynomial, rational or global analytical first integral. © 2013 Elsevier Inc.

Original language	English
Pages (from-to)	3185-3204
Journal	Journal of Differential Equations
Volume	255
Issue number	10
DOIs	https://doi.org/10.1016/j.jde.2013.07.032
Publication status	Published - 15 Nov 2013

Keywords

Analytic first integral
Polynomial first integral
Quasi-homogeneous polynomial differential system
Quasi-homogeneous polynomial vector field

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https://ddd.uab.cat/record/150591

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abstract = "In this paper we study the quasi-homogeneous polynomial differential systems and provide an algorithm for obtaining all these systems with a given degree. Using this algorithm we obtain all quasi-homogeneous vector fields of degree 2 and 3.The quasi-homogeneous polynomial differential systems are Liouvillian integrable. In particular, we characterize all the quasi-homogeneous vector fields of degree 2 and 3 having a polynomial, rational or global analytical first integral. {\textcopyright} 2013 Elsevier Inc.",

keywords = "Analytic first integral, Polynomial first integral, Quasi-homogeneous polynomial differential system, Quasi-homogeneous polynomial vector field",

author = "Bel{\'e}n Garc{\'i}a and Jaume Llibre and {P{\'e}rez del R{\'i}o}, {Jes{\'u}s S.}",

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T1 - Planar quasi-homogeneous polynomial differential systems and their integrability

AU - García, Belén

AU - Llibre, Jaume

AU - Pérez del Río, Jesús S.

PY - 2013/11/15

Y1 - 2013/11/15

N2 - In this paper we study the quasi-homogeneous polynomial differential systems and provide an algorithm for obtaining all these systems with a given degree. Using this algorithm we obtain all quasi-homogeneous vector fields of degree 2 and 3.The quasi-homogeneous polynomial differential systems are Liouvillian integrable. In particular, we characterize all the quasi-homogeneous vector fields of degree 2 and 3 having a polynomial, rational or global analytical first integral. © 2013 Elsevier Inc.

AB - In this paper we study the quasi-homogeneous polynomial differential systems and provide an algorithm for obtaining all these systems with a given degree. Using this algorithm we obtain all quasi-homogeneous vector fields of degree 2 and 3.The quasi-homogeneous polynomial differential systems are Liouvillian integrable. In particular, we characterize all the quasi-homogeneous vector fields of degree 2 and 3 having a polynomial, rational or global analytical first integral. © 2013 Elsevier Inc.

KW - Analytic first integral

KW - Polynomial first integral

KW - Quasi-homogeneous polynomial differential system

KW - Quasi-homogeneous polynomial vector field

U2 - https://doi.org/10.1016/j.jde.2013.07.032

DO - https://doi.org/10.1016/j.jde.2013.07.032

M3 - Article

SN - 0022-0396

VL - 255

SP - 3185

EP - 3204

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 10

ER -

Planar quasi-homogeneous polynomial differential systems and their integrability

Abstract

Keywords

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