Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves

Jaume Llibre, Marcelo Messias, Alisson C. Reinol

Research output: Contribution to journalArticleResearchpeer-review

Abstract

© 2016 Informa UK Limited, trading as Taylor & Francis Group. In this paper, we give the normal form of all planar polynomial vector fields of degree d ≤ 3 having two nonconcentric circles C1 and C2 as invariant algebraic curves and the function H=Cβ1 Cα2, with α and β real values, as first integral. Moreover, we classify all global phase portraits on the Poincaré disc of a subclass of these vector fields.
Original languageEnglish
Pages (from-to)374-390
JournalDynamical Systems
Volume32
Issue number3
DOIs
Publication statusPublished - 3 Jul 2017

Keywords

  • Poincaré compactification
  • Quadratic and cubic vector fields
  • global analysis
  • invariant algebraic curves
  • limit cycles
  • normal forms

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