Configurations of limit cycles and planar polynomial vector fields

Jaume Llibre; Gerardo Rodríguez

doi:https://doi.org/10.1016/j.jde.2003.10.008

Configurations of limit cycles and planar polynomial vector fields

Jaume Llibre, Gerardo Rodríguez

Department of Mathematics

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

55 Citations (Scopus)

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. © 2003 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	374-380
Journal	Journal of Differential Equations
Volume	198
DOIs	https://doi.org/10.1016/j.jde.2003.10.008
Publication status	Published - 10 Apr 2004

Keywords

Limit cycles
Quadratic vector fields

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AU - Rodríguez, Gerardo

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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

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DO - https://doi.org/10.1016/j.jde.2003.10.008

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