Computer-assisted techniques for the verification of the Chebyshev property of Abelian integrals
2013 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 254, no 8, 3647-3663 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2013. Vol. 254, no 8, 3647-3663 p.
Hilbert's 16th problem, Chebyshev systems, Abelian integrals, Rigorous computer methods
IdentifiersURN: urn:nbn:se:uu:diva-197951DOI: 10.1016/j.jde.2013.01.036ISI: 000315831000020OAI: oai:DiVA.org:uu-197951DiVA: diva2:615414