Classification of centers, their cyclicity and isochronicity for a class of polynomial differential systems of degree d ≥ 7 odd

Jaume Llibre, Claudia Valls

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Abstract

In this paper we classify the centers, the cyclicity of its Hopf bifurcation and the isochronicity of the polynomial differential systems in ℝ2 of degree d ≥ 7 odd that in complex notation z = x + iy can be written as Ż = (λ + i)z + (zž)d-7/2 (Az6Z̄ + Bz4z̄3 + Cz 2Z̄5 + Dz̄7), where λ ∈ ℝ, and A, B, C, D ∈ C.
Original languageEnglish
Pages (from-to)859-873
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Volume17
Issue number5 SUPPL.
Publication statusPublished - 1 Dec 2010

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