Electron. J. Differential Equations, Vol. 2018 (2018), No. 83, pp. 1-7.

Normal forms and hyperbolic algebraic limit cycles for a class of polynomial differential systems

Jaume Llibre, Claudia Valls

We study the normal forms of polynomial systems having a set of invariant algebraic curves with singular points. We provide sufficient conditions for the existence of hyperbolic algebraic limit cycles.

Submitted March 3, 2017. Published March 31, 2018.
Math Subject Classifications: 34C05, 34A34, 34C14.
Key Words: Limit cycles; polynomial vector fields; algebraic limit cycles.

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Jaume Llibre
Departament de Matemàtiques
Universitat Aut&ogfrave;noma de Barcelona
08193 Bellaterra, Barcelona, Catalonia, Spain
email: jllibre@mat.uab.cat
  Claudia Valls
Departamento de Matemática
Instituto Superior Técnico
Universidade de Lisboa
1049-001 Lisboa, Portugal
email: cvalls@math.ist.utl.pt

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