On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves

Jaume Llibre, Rafael Ramírez, Natalia Sadovskaia

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22 Citations (Scopus)

Abstract

We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial vector field of degree n can exhibit if the vector field has exactly k nonsingular irreducible invariant algebraic curves. Additionally we provide sufficient conditions in order that all the algebraic limit cycles are hyperbolic. We also provide lower bounds for N. © 2010 Elsevier Inc.
Original languageEnglish
Pages (from-to)983-999
JournalJournal of Differential Equations
Volume250
DOIs
Publication statusPublished - 15 Jan 2011

Keywords

  • 16th Hilbert problem
  • Algebraic limit cycles
  • Limit cycles
  • Polynomial vector fields

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