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Zeitschrift für angewandte Mathematik und Physik

, Volume 65, Issue 6, pp 1127–1136 | Cite as

Darboux invariants for planar polynomial differential systems having an invariant conic

  • Jaume Llibre
  • Marcelo Messias
  • Alisson C. Reinol
Article

Abstract

We characterize all the planar polynomial differential systems with a unique invariant algebraic curve given by a real conic and having a Darboux invariant.

Mathematics Subject Classification (2010)

34C05 34C99 

Keywords

Polynomial differential systems Invariant conics Darboux integrability Darboux invariant 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Jaume Llibre
    • 1
  • Marcelo Messias
    • 2
  • Alisson C. Reinol
    • 2
  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain
  2. 2.Departamento de Matemática e ComputaçãoFCT–UNESPSão PauloBrazil

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