We study singularity confinement phenomena in examples of delay-differential Painlevé equations, which involve shifts and derivatives with respect to a single independent variable. We propose a geometric interpretation of our results in terms of mappings between jet spaces, defining certain singularities analogous to those of interest in the singularity analysis of discrete systems, and what it means for them to be confined. For three previously studied examples of delay-differential Painlevé equations, we describe all such singularities and show they are confined in the sense of our geometric description.

中文翻译：

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时滞微分Painlevé方程的奇异性限制

我们在时滞微分Painlevé方程的示例中研究奇异约束现象，该方程涉及相对于单个自变量的移位和导数。我们用射流空间之间的映射来对结果进行几何解释，定义类似于离散系统奇异性分析中所关注的奇异性以及对其加以限制的含义。对于三个先前研究的延迟微分Painlevé方程示例，我们描述了所有这样的奇点，并表明它们在我们的几何描述的意义上是受限的。