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Computer-assisted techniques for the verification of the Chebyshev property of Abelian integrals
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
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
Abstract [en]

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.
Keyword [en]
Hilbert's 16th problem, Chebyshev systems, Abelian integrals, Rigorous computer methods
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:uu:diva-197951DOI: 10.1016/j.jde.2013.01.036ISI: 000315831000020OAI: oai:DiVA.org:uu-197951DiVA: diva2:615414
Available from: 2013-04-10 Created: 2013-04-08 Last updated: 2017-12-06Bibliographically approved

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Figueras, Jordi-LluisTucker, Warwick

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