Darbouxian integrability of polynomial vector fields with special emphasis on the two-dimensional surfaces

Jaume Llibre; Gerardo Rodríguez

doi:https://doi.org/10.1142/S0218127402006187

Darbouxian integrability of polynomial vector fields with special emphasis on the two-dimensional surfaces

Jaume Llibre, Gerardo Rodríguez

Department of Mathematics

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

5 Citations (Scopus)

Abstract

A survey on the Darbouxian theory of integrability for real polynomial vector fields in the plane is presented. The theory is then extended to real polynomial vector fields on two-dimensional surfaces, more specifically on the quadratics and on the two-dimensional torus. The notion of a polynomial vector field on a regular surface and the notion of a first integral for such vector fields are defined.

Original language	English
Pages (from-to)	2821-2833
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	12
DOIs	https://doi.org/10.1142/S0218127402006187
Publication status	Published - 1 Jan 2002

Keywords

Integrability
Polynomial vector fields

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https://doi.org/10.1142/S0218127402006187

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title = "Darbouxian integrability of polynomial vector fields with special emphasis on the two-dimensional surfaces",

abstract = "A survey on the Darbouxian theory of integrability for real polynomial vector fields in the plane is presented. The theory is then extended to real polynomial vector fields on two-dimensional surfaces, more specifically on the quadratics and on the two-dimensional torus. The notion of a polynomial vector field on a regular surface and the notion of a first integral for such vector fields are defined.",

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author = "Jaume Llibre and Gerardo Rodr{\'i}guez",

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AU - Rodríguez, Gerardo

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N2 - A survey on the Darbouxian theory of integrability for real polynomial vector fields in the plane is presented. The theory is then extended to real polynomial vector fields on two-dimensional surfaces, more specifically on the quadratics and on the two-dimensional torus. The notion of a polynomial vector field on a regular surface and the notion of a first integral for such vector fields are defined.

AB - A survey on the Darbouxian theory of integrability for real polynomial vector fields in the plane is presented. The theory is then extended to real polynomial vector fields on two-dimensional surfaces, more specifically on the quadratics and on the two-dimensional torus. The notion of a polynomial vector field on a regular surface and the notion of a first integral for such vector fields are defined.

KW - Integrability

KW - Polynomial vector fields

U2 - https://doi.org/10.1142/S0218127402006187

DO - https://doi.org/10.1142/S0218127402006187

M3 - Article

VL - 12

SP - 2821

EP - 2833

ER -

Darbouxian integrability of polynomial vector fields with special emphasis on the two-dimensional surfaces

Abstract

Keywords

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