Hilbert's Sixteenth Problem for Polynomial Liénard Equations

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Abstract

This article reports on the survey talk 'Hilbert's Sixteenth Problem for Liénard equations,' given by the author at the Oberwolfach Mini-Workshop 'Algebraic and Analytic Techniques for Polynomial Vector Fields.' It is written in a way that it is accessible to a public with heterogeneous mathematical background. The article reviews recent developments and techniques used in the study of Hilbert's 16th problem where the main focus is put on the subclass of polynomial vector fields derived from the Liérd equations. © 2012 Springer Basel AG.
Original languageEnglish
Pages (from-to)3-18
JournalQualitative Theory of Dynamical Systems
Volume11
Issue number1
DOIs
Publication statusPublished - 1 Dec 2012

Keywords

  • Compactification
  • Large amplitude limit cycles
  • Liénard equations
  • Periodic orbits
  • Planar vector fields

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