Summability of canard-heteroclinic saddle connections

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Kenens, Karel¹ 

[1] Hasselt Univ, Dept Math, Martelarenlaan 42, B-3500 Hasselt, Belgium

关键词: Gevrey series;    Borel summation;    Slow-fast systems;    Singular perturbations;    Canards;   

DOI  :  10.1016/j.jde.2016.08.030

来源: Elsevier

【 摘 要 】

For a given (real analytic) slow-fast system {(x) over dot = epsilon f(x, y, epsilon) (y) over dot =g(x, y, epsilon), that admits a slow-fast saddle and that satisfies some mild assumptions, the Borel-summability properties of the saddle separatrix tangent in the direction of the critical curve are investigated: 1-summability is shown. It is also shown that slow-fast saddle connections of canard type have summability properties, in contrast to the typical lack of Borel-summability for canard solutions of general equations. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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