On the Chebyshev property of certain abelian integrals near a polycycle (Q1641856)

This paper is concerned with the problem when a collection of abelian integrals forms an extended complete Chebyshev system. This type of problems arises in the context of the so-called infinitesimal Hilbert's 16th problem proposed by Arnold. In the present paper, the authors are interested in a conjecture formulated by Dumortier and Roussarie, where singular perturbation problems occurring in planar slow-fast systems depending on parameters are considered.