Structural stability of planar polynomial foliations

Xavier Jarque, Jaume Llibre, Douglas S. Shafer

Research output: Contribution to journalReview articleResearchpeer-review

2 Citations (Scopus)

Abstract

We discuss natural notions of structural stability of planar polynomial foliations of fixed degree with respect to perturbation within the same restricted set, within the set of all polynomial vector fields of the same degree, and within the set of smooth vector fields. Characterization theorems for structural stability in the latter two settings are obtained as immediate corollaries of known results. We provide sufficient conditions and separate necessary conditions for structural stability of planar polynomial foliations with respect to perturbation within the set of planar polynomial foliations of the same degree. © 2005 Springer Science+Business Media, Inc.
Original languageEnglish
Pages (from-to)573-587
JournalJournal of Dynamics and Differential Equations
Volume17
Issue number3
DOIs
Publication statusPublished - 1 Jul 2005

Keywords

  • Foliation
  • Polynomial vector field
  • Structural stability

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