Cyclicity of a simple focus via the vanishing multiplicity of inverse integrating factors

Isaac A. García, Jaume Llibre, Susanna Maza

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

First we provide new properties about the vanishing multiplicity of the inverse integrating factor of a planar analytic differential system at a focus. After we use this vanishing multiplicity for studying the cyclicity of foci with pure imaginary eigenvalues and with homogeneous nonlinearities of arbitrary degree having either its radial or angular speed independent of the angle variable in polar coordinates. After we study the cyclicity of a class of nilpotent foci in their analytic normal form. © 2013 Elsevier Inc.
Original languageEnglish
Pages (from-to)3880-3896
JournalJournal of Differential Equations
Volume255
Issue number11
DOIs
Publication statusPublished - 1 Dec 2013

Keywords

  • Center
  • Cyclicity of a focus
  • Focus
  • Inverse integrating factor
  • Limit cycles
  • Vanishing multiplicity

Fingerprint Dive into the research topics of 'Cyclicity of a simple focus via the vanishing multiplicity of inverse integrating factors'. Together they form a unique fingerprint.

  • Cite this