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

Jordi Lluís Figueras; Warwick Tucker; Jordi Villadelprat

doi:10.1016/j.jde.2013.01.036

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

Jordi Lluís Figueras, Warwick Tucker, Jordi Villadelprat

Research output: Contribution to journal › Article › Research › peer-review

20 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 language	English
Pages (from-to)	3647-3663
Number of pages	17
Journal	Journal of Differential Equations
Volume	254
Issue number	8
DOIs	https://doi.org/10.1016/j.jde.2013.01.036
Publication status	Published - 15 Apr 2013
Externally published	Yes

Keywords

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

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10.1016/j.jde.2013.01.036

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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.",

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AU - Figueras, Jordi Lluís

AU - Tucker, Warwick

AU - Villadelprat, Jordi

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Y1 - 2013/4/15

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AB - 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.

KW - Abelian integrals

KW - Chebyshev systems

KW - Hilbert's 16th problem

KW - Rigorous computer methods

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EP - 3663

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 8

ER -

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

Abstract

Keywords

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