非一般转折点附近平面鸭式解的渐近展开
Asymptotic expansion of planar canard solutions near a non-generic turning point
摘要：
本文讨论了在研究实奇摄动常微分方程时出现的鸭式解的渐近性。这些解决方案从“慢曲线”的吸引分支附近开始，在跟随“慢曲线”的排斥分支一段时间之前，正在越过一个转折点。假设转折点是退化的（或非通用的），我们应用在最近的一篇论文中提出的对应关系。该应用需要定义在第一部分中研究的一族函数$ϕ$。然后，我们利用对应关系计算鸭式解的小参数幂的渐近展开。
英文摘要：
This paper deals with the asymptotic study of the so-called canard solutions, which arise in the study of real singularly perturbed ODEs. Starting near an attracting branch of the "slow curve", those solutions are crossing a turning point before following for a while a repelling branch of the "slow curve". Assuming that the turning point is degenerate (or non-generic), we apply a correspondence presented in a recent paper. This application needs the definition of a family of functions $ϕ$ that is studied in a first part. Then, we use the correspondence is used to compute the asymptotic expansion in the powers of the small parameter for the canard solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
