We study the distribution of the sequence of elements of the discrete dynamical system generated by iterations of the Möbius map \(x \mapsto (ax + b)/(cx+d)\) over a finite field of p elements at the moments of time that correspond to prime numbers. In particular, we obtain nontrivial estimates of exponential sums with such sequences.

中文翻译：

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关于黄金时段Möbius变换生成的动力学系统

我们研究了由Möbius映射\（x \ mapsto（ax + b）/（cx + d）\）的迭代生成的离散动力学系统的元素序列在p元素的有限域上的分布。与素数相对应的时间。特别地，我们获得了具有此类序列的指数和的非平凡估计。