On the Chebyshev property of certain Abelian integrals near a polycycle
Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)

Date:	2018
Abstract:	F. Dumortier and R. Roussarie formulated in (Discrete Contin. Dyn. Syst. 2 (2009) 723-781] a conjecture concerning the Chebyshev property of a collection I₀,I₁,. . . ,In of Abelian integrals arising from singular perturbation problems occurring in planar slow-fast systems. The aim of this note is to show the validity of this conjecture near the polycycle at the boundary of the family of ovals defining the Abelian integrals. As a corollary of this local result we get that the linear span ⟨I₀,I₁,. . . ,In⟩ is Chebyshev with accuracy k = k(n).
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Abelian integrals ; Chebyshev system ; Wronskian
Published in:	Qualitative theory of dynamical systems, Vol. 17, issue 1 (April 2018) , p. 261-270, ISSN 1662-3592

DOI: 10.1007/s12346-017-0226-3

Postprint 8 p, 483.6 KB

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