The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems

Hector Giacomini, Jaume Giné, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

62 Citations (Scopus)

Abstract

In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré-Liapunov method to find linear type centers can be also used to find the nilpotent centers. Moreover, we show that the degenerate centers which are limit of linear type centers are also detectable with the Poincaré-Liapunov method. © 2006 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)406-426
JournalJournal of Differential Equations
Volume227
DOIs
Publication statusPublished - 15 Aug 2006

Keywords

  • Cyclicity
  • Degenerate center
  • Liapunov constants
  • Nilpotent center

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