On the number of limit cycles bifurcating from a non-global degenerated center

Armengol Gasull, Chengzhi Li, Changjian Liu

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8 Citations (Scopus)

Abstract

We give an upper bound for the number of zeros of an Abelian integral. This integral controls the number of limit cycles that bifurcate, by a polynomial perturbation of arbitrary degree n, from the periodic orbits of the integrable system (1 + x) d H = 0, where H is the quasi-homogeneous Hamiltonian H (x, y) = x2 k / (2 k) + y2 / 2. The tools used in our proofs are the Argument Principle applied to a suitable complex extension of the Abelian integral and some techniques in real analysis. © 2006 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)268-280
JournalJournal of Mathematical Analysis and Applications
Volume329
DOIs
Publication statusPublished - 1 May 2007

Keywords

  • Abelian integral
  • Degenerated center
  • Limit cycle
  • Planar vector field

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