On the number of limit cycles surrounding a unique singular point for polynomial differential systems of arbitrary degree

Belén García, Jaume Llibre, Jesús S. Pérez del Río

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4 Citations (Scopus)

Abstract

We study the number of limit cycles that bifurcate from the periodic orbits of the center over(x, ̇) = - y R (x, y), over(y, ̇) = x R (x, y) where R is a convenient polynomial of degree 2, when we perturb it inside the class of all polynomial differential systems of degree n. We use averaging theory for computing this number. As a consequence of our study we provide the biggest number of limit cycles surrounding a unique singular point in terms of the degree of the system, known up to now. © 2007 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)4461-4469
JournalNonlinear Analysis, Theory, Methods and Applications
Volume69
DOIs
Publication statusPublished - 15 Dec 2008

Keywords

  • Averaging theory
  • Bifurcation from a center
  • Limit cycle

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