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On the Chebyshev property of certain Abelian integrals near a polycycle
时间  Datetime
2017-07-19 14:30 — 16:00 
地点  Venue
Middle Lecture Room
报告人  Speaker
Prof. Jordi Villadelprat
单位  Affiliation
Universitat Rovira i Virgili, Spain
邀请人  Host
张祥
报告摘要  Abstract

Dumortier and R. Roussarie formulated in [Birth of canard cycles, Discrete Contin. Dyn. Syst. 2 (2009), 723-781] a conjecture concerning the Chebyshev property of a collection $I_0,I_1,\ldots,I_n$ of Abelian integrals arising from singular perturbation problems occurring in planar slow-fast systems. The aim of this talk 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 of $I_0,I_1,\ldots,I_n$ is Chebyshev with accuracy $k=k(n).$ This result is a joint work with David Marín (UAB).