Restricted independence in displacement function for better estimation of cyclicity

Xingwu Chen, Jaume Llibre, Zhaoxia Wang, Weinian Zhang

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

2 Citations (Scopus)

Abstract

© 2017 Elsevier Inc. Since the independence of focal values is a sufficient condition to give a number of limit cycles arising from a center-focus equilibrium, in this paper we consider a restricted independence to a parametric curve, which gives a method not only to increase the lower bound for the cyclicity of the center-focus equilibrium but also to be available when those focal values are not independent. We apply this method to a nondegenerate cubic center-focus variety and prove that the cyclicity reaches its an upper bound.
Original languageEnglish
Pages (from-to)5773-5791
JournalJournal of Differential Equations
Volume262
Issue number12
DOIs
Publication statusPublished - 15 Jun 2017

Keywords

  • Center-focus variety
  • Cyclicity
  • Focal value
  • Independence
  • Power sequence

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    Chen, X., Llibre, J., Wang, Z., & Zhang, W. (2017). Restricted independence in displacement function for better estimation of cyclicity. Journal of Differential Equations, 262(12), 5773-5791. https://doi.org/10.1016/j.jde.2017.02.015