In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the function. In this paper we reverse the direction of this study. In particular, restricting to the complex plane, we start with a sequence of complex numbers and study the functions (if any) for which this sequence is an orbit under iteration. This gives rise to questions of existence and of uniqueness. We resolve some questions, and show that these issues can be quite delicate.

中文翻译：

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哪些序列是轨道？

在离散动力系统的研究中，我们通常从一个函数开始，从空间到其自身，并询问有关函数迭代序列的性质的问题。在本文中，我们颠倒了本研究的方向。特别是，限制在复杂平面上，我们从一个复数序列开始，并研究该序列为其迭代轨道的函数（如果有）。这引起了存在性和独特性的问题。我们解决了一些问题，并表明这些问题可能非常棘手。