Darboux integrability and reversible quadratic vector fields

Jaume Llibre; João Carlos Medrado

doi:https://doi.org/10.1216/rmjm/1181069627

Darboux integrability and reversible quadratic vector fields

Jaume Llibre, João Carlos Medrado

Department of Mathematics

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

15 Citations (Scopus)

Abstract

In this paper we improve the Darboux theory of integrability for reversible polynomial vector fields in Rn, and we classify the phase portraits of all φ-reversible quadratic polynomial vector fields of R2 such that the dimension of the set of fixed points of φ is equal to one. Copyright ©2005 Rocky Mountain Mathematics Consortium.

Original language	English
Pages (from-to)	1999-2057
Journal	Rocky Mountain Journal of Mathematics
Volume	35
DOIs	https://doi.org/10.1216/rmjm/1181069627
Publication status	Published - 1 Dec 2005

Keywords

Darboux integrability
Reversible vector fields

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https://doi.org/10.1216/rmjm/1181069627

Cite this

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title = "Darboux integrability and reversible quadratic vector fields",

abstract = "In this paper we improve the Darboux theory of integrability for reversible polynomial vector fields in Rn, and we classify the phase portraits of all φ-reversible quadratic polynomial vector fields of R2 such that the dimension of the set of fixed points of φ is equal to one. Copyright {\textcopyright}2005 Rocky Mountain Mathematics Consortium.",

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AU - Llibre, Jaume

AU - Medrado, João Carlos

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AB - In this paper we improve the Darboux theory of integrability for reversible polynomial vector fields in Rn, and we classify the phase portraits of all φ-reversible quadratic polynomial vector fields of R2 such that the dimension of the set of fixed points of φ is equal to one. Copyright ©2005 Rocky Mountain Mathematics Consortium.

KW - Darboux integrability

KW - Reversible vector fields

U2 - https://doi.org/10.1216/rmjm/1181069627

DO - https://doi.org/10.1216/rmjm/1181069627

M3 - Article

VL - 35

SP - 1999

EP - 2057

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

SN - 0035-7596

ER -

Darboux integrability and reversible quadratic vector fields

Abstract

Keywords

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