Classification of the centers and isochronous centers for a class of quartic-like systems

Jaume Llibre, Clàudia Valls

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15 Citations (Scopus)

Abstract

In this paper we classify the centers and isochronous centers for a class of polynomial differential systems in R2 of degree d that in complex notation z = x + i y can be written as over(z, ̇) = i z + (z over(z, -))frac(d - 4, 2) (A z3 over(z, -) + B z2 over(z, -)2 + C over(z, -)4), where d ≥ 4 is an arbitrary even positive integer and A, B, C ∈ C. Note that if d = 4 we obtain a special case of quartic polynomial differential systems which can have a center at the origin. © 2009 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)3119-3128
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
DOIs
Publication statusPublished - 1 Oct 2009

Keywords

  • Centers
  • Isochronous centers
  • Quartic polynomial vector field

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