Structurally stable quadratic foliations

Xavier Jarque, Jaume Llibre, Douglas S. Shafer

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)


We characterize the elements of Fn, the set of polynomial vector fields on the plane of degree at most n without finite singular points, that are structurally stable with respect to perturbations within Fn for n ≤ 2. We do so with respect to each of the two natural definitions of stability in this setting. Copyright © 2008 Rocky Mountain Mathematics Consortium.
Original languageEnglish
Pages (from-to)489-530
JournalRocky Mountain Journal of Mathematics
Publication statusPublished - 1 Jan 2008


  • Phase portraits
  • Quadratic foliations
  • Quadratic vector fields
  • Structural stability


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