Darboux integrability of polynomial differential systems in ℝ3

Jaume Llibre; Clàudia Valls

Darboux integrability of polynomial differential systems in ℝ³

Jaume Llibre, Clàudia Valls

Departament de Matemàtiques

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Resum

In this article we study the Darboux integrability of the polynomial differential systems x = y- x2, y; = z- x, z =-d- ax- by- cz. This system comes from the study of a Hopf bifurcation in slow-fast systems with two slow variables and one fast variable. The tools used here for studying the Darboux integrability can be applied to arbitrary polynomial differential systems in ℝ3.

Idioma original	Anglès
Pàgines (de-a)	603-619
Revista	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volum	20
Número	4
Estat de la publicació	Publicada - 1 de gen. 2013

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https://www.scopus.com/pages/publications/84896343271

Com citar-ho

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title = "Darboux integrability of polynomial differential systems in ℝ3",

abstract = "In this article we study the Darboux integrability of the polynomial differential systems x = y- x2, y; = z- x, z =-d- ax- by- cz. This system comes from the study of a Hopf bifurcation in slow-fast systems with two slow variables and one fast variable. The tools used here for studying the Darboux integrability can be applied to arbitrary polynomial differential systems in ℝ3.",

keywords = "Darboux integrability, Darboux polynomial, Invariants",

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

year = "2013",

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language = "English",

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journal = "Bulletin of the Belgian Mathematical Society - Simon Stevin",

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TY - JOUR

T1 - Darboux integrability of polynomial differential systems in ℝ3

AU - Llibre, Jaume

AU - Valls, Clàudia

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this article we study the Darboux integrability of the polynomial differential systems x = y- x2, y; = z- x, z =-d- ax- by- cz. This system comes from the study of a Hopf bifurcation in slow-fast systems with two slow variables and one fast variable. The tools used here for studying the Darboux integrability can be applied to arbitrary polynomial differential systems in ℝ3.

AB - In this article we study the Darboux integrability of the polynomial differential systems x = y- x2, y; = z- x, z =-d- ax- by- cz. This system comes from the study of a Hopf bifurcation in slow-fast systems with two slow variables and one fast variable. The tools used here for studying the Darboux integrability can be applied to arbitrary polynomial differential systems in ℝ3.

KW - Darboux integrability

KW - Darboux polynomial

KW - Invariants

UR - https://www.scopus.com/pages/publications/84896343271

M3 - Article

SN - 1370-1444

VL - 20

SP - 603

EP - 619

JO - Bulletin of the Belgian Mathematical Society - Simon Stevin

JF - Bulletin of the Belgian Mathematical Society - Simon Stevin

IS - 4

ER -

Darboux integrability of polynomial differential systems in ℝ3

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Darboux integrability of polynomial differential systems in ℝ³