The transit time of mean-median orbits – the time it takes for an orbit to become stationary – has been conjectured to be finite but unbounded over the rationals. Through a study of some near-regular structures in these orbits, we construct two non-trivial sequences of initial sets of increasing size for which the transit time grows linearly and quadratically, respectively, with the size of the set.

中文翻译：

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关于平均中位轨道凌日时间的无界性

平均中值轨道的通过时间——轨道变为静止所需的时间——被认为是有限的，但在有理数上是无界的。通过对这些轨道中一些近规则结构的研究，我们构建了两个非平凡的初始集大小序列，其中传输时间分别随集的大小线性和二次增长。