Configurations of limit cycles and planar polynomial vector fields

Jaume Llibre; Gerardo Rodríguez

doi:10.1016/j.jde.2003.10.008

Configurations of limit cycles and planar polynomial vector fields

Jaume Llibre, Gerardo Rodríguez

Departamento de Matemáticas

Producción científica: Contribución a una revista › Artículo › Investigación › revisión exhaustiva

68 Citas (Scopus)

Resumen

We show that every finite configuration of disjoint simple closed curves of the plane is topologically realizable as the set of limit cycles of a polynomial vector field. Moreover, the realization can be made by algebraic limit cycles, and we provide an explicit polynomial vector field exhibiting any given finite configuration of limit cycles. © 2003 Elsevier Inc. All rights reserved.

Idioma original	Inglés
Páginas (desde-hasta)	374-380
Publicación	Journal of Differential Equations
Volumen	198
DOI	https://doi.org/10.1016/j.jde.2003.10.008
Estado	Publicada - 10 abr 2004

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title = "Configurations of limit cycles and planar polynomial vector fields",

abstract = "We show that every finite configuration of disjoint simple closed curves of the plane is topologically realizable as the set of limit cycles of a polynomial vector field. Moreover, the realization can be made by algebraic limit cycles, and we provide an explicit polynomial vector field exhibiting any given finite configuration of limit cycles. {\textcopyright} 2003 Elsevier Inc. All rights reserved.",

keywords = "Limit cycles, Quadratic vector fields",

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

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T1 - Configurations of limit cycles and planar polynomial vector fields

AU - Llibre, Jaume

AU - Rodríguez, Gerardo

PY - 2004/4/10

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N2 - We show that every finite configuration of disjoint simple closed curves of the plane is topologically realizable as the set of limit cycles of a polynomial vector field. Moreover, the realization can be made by algebraic limit cycles, and we provide an explicit polynomial vector field exhibiting any given finite configuration of limit cycles. © 2003 Elsevier Inc. All rights reserved.

AB - We show that every finite configuration of disjoint simple closed curves of the plane is topologically realizable as the set of limit cycles of a polynomial vector field. Moreover, the realization can be made by algebraic limit cycles, and we provide an explicit polynomial vector field exhibiting any given finite configuration of limit cycles. © 2003 Elsevier Inc. All rights reserved.

KW - Limit cycles

KW - Quadratic vector fields

UR - https://www.scopus.com/pages/publications/12144290753

U2 - 10.1016/j.jde.2003.10.008

DO - 10.1016/j.jde.2003.10.008

M3 - Article

SN - 0022-0396

VL - 198

SP - 374

EP - 380

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Configurations of limit cycles and planar polynomial vector fields

Resumen

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