AI 中文总结
该研究针对极小系统中多项式返回时间集，对已有结构结果进行精细化，证明可将无限步幂零因子替换为极大 k 步幂零因子，k 依赖给定多项式，其与多项式的Host - Kra 复杂度有关。
AI 中文摘要
我们证明了Glasscock、Koutsogiannis、Le、Moreira、Richter和Robertson近期在拓扑动力学中一个结构结果的精细化。他们表明在极小系统中，多项式返回时间与其极大无限步幂零因子中的返回时间在非分段 syndetic 集上不同。特别地，我们证明无限步幂零因子可被系统的极大 k 步幂零因子替代，其中 k 仅依赖给定多项式，k - 1 等于多项式的Host - Kra 复杂度。
英文摘要
We prove a refinement of a recent structural result in topological dynamics due to Glasscock, Koutsogiannis, Le, Moreira, Richter, and Robertson, who showed that in a minimal system, polynomial return-times differ by non-piecewise syndetic sets from those in its maximal infinite-step pronilfactor. In particular, we prove that the infinite-step pronilfactor can be replaced by the maximal $k$-step pronilfactor of the system, where $k$ depends only on the given polynomials, with $k-1$ being equal to the Host-Kra complexity of the polynomials.
Comments22 pages
