Computer-assisted techniques for the verification of the Chebyshev property of Abelian integrals

Jordi Lluís Figueras, Warwick Tucker, Jordi Villadelprat

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17 Citations (Scopus)

Abstract

We develop techniques for the verification of the Chebyshev property of Abelian integrals. These techniques are a combination of theoretical results, analysis of asymptotic behavior of Wronskians, and rigorous computations based on interval arithmetic. We apply this approach to tackle a conjecture formulated by Dumortier and Roussarie in [F. Dumortier, R. Roussarie, Birth of canard cycles, Discrete Contin. Dyn. Syst. 2 (2009) 723-781], which we are able to prove for q≤. 2.

Original languageEnglish
Pages (from-to)3647-3663
Number of pages17
JournalJournal of Differential Equations
Volume254
Issue number8
DOIs
Publication statusPublished - 15 Apr 2013
Externally publishedYes

Keywords

  • Abelian integrals
  • Chebyshev systems
  • Hilbert's 16th problem
  • Rigorous computer methods

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