A restricted version of Hilbert's 16th problem for quadratic vector fields

Yu Ilyashenko, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

The restricted version of Hilbert's 16th problem for quadratic vector fields requires an upper estimate of the number of limit cycles through a vector parameter that characterizes the vector fields considered and the limit cycles to be counted. In this paper we give an upper estimate of the number of limit cycles of quadratic vector fields V-distant from centers and K-distant from singular quadratic vector fields provided that the limit cycles are "5-distant from singular points and infinity". © 2010 Independent University of Moscow.
Original languageEnglish
Pages (from-to)317-335
JournalMoscow Mathematical Journal
Volume10
Issue number2
Publication statusPublished - 1 Dec 2010

Keywords

  • Limit cycles
  • Quadratic systems

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