Darboux integrability of polynomial differential systems in R^3

Jaume Llibre; Clàudia Valls

Darboux integrability of polynomial differential systems in R^3

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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)	0603-619
Nombre de pàgines	17
Revista	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volum	20
Estat de la publicació	Publicada - 2013

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https://ddd.uab.cat/record/150588

Sistemas dinámicos contínuos y discretos: bifurcaciones, orbitas periódicas, integrabilidad y aplicaciones
Torregrosa i Arús, J. (Investigador/a principal), Cima Mollet, A. M. (Investigador/a), Gasull Embid, A. (Investigador/a), Cors Iglesias, J. M. (Investigador/a), Mañosa Fernández, V. (Investigador/a), Artes Ferragud, J. C. (Investigador/a), Llibre Salo, J. (Investigador/a), Corbera Subirana, M. (Investigador/a), Pantazi ., C. (Investigador/a), Garrido Pelaez, J. M. (Col.laborador/a), Mañosas Capellades, F. (Col.laborador/a), Jimenez Ruiz, J. J. (Col.laborador/a), Mayayo Cortasa, T. (Col.laborador/a) & Villadelprat Yague, J. (Investigador/a)
Fons Social Europeu
1/09/23 → 31/08/26
Projecte: Projectes i Ajuts a la Recerca

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title = "Darboux integrability of polynomial differential systems in R\textasciicircum{}3",

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, Invariants, Darboux polynomial",

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

year = "2013",

language = "English",

volume = "20",

pages = "0603--619",

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

issn = "1370-1444",

publisher = "Belgian Mathematical Society",

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T1 - Darboux integrability of polynomial differential systems in R^3

AU - Llibre, Jaume

AU - Valls, Clàudia

PY - 2013

Y1 - 2013

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 - Invariants

KW - Darboux polynomial

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

ER -

Darboux integrability of polynomial differential systems in R^3

Resum

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Sistemas dinámicos contínuos y discretos: bifurcaciones, orbitas periódicas, integrabilidad y aplicaciones

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