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

• 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.

Nyckelord

Hilbert's 16th problem

Chebyshev systems

Abelian integrals

Rigorous computer methods

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