This paper is devoted to the study of the analytic properties of Mahler systems at 0. We give an effective characterisation of Mahler systems that are regular singular at 0, that is, systems which are equivalent to constant ones. Similar characterisations already exist for differential and (q-)difference systems but they do not apply in the Mahler case. This work fill in the gap by giving an algorithm which decides whether or not a Mahler system is regular singular at 0.

中文翻译：

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确定规则奇异Mahler系统的算法

本文致力于研究在0时的Mahler系统的解析性质。我们给出了在0时为规则奇异的Mahler系统的有效刻画，即等效于常数的系统。微分和（q）差分系统已经存在类似的特征，但不适用于Mahler情况。这项工作通过提供一种算法来填补空白，该算法确定Mahler系统是否为0的规则奇异点。