论文标题
最小的系统有限许多千古的措施
Minimal systems with finitely many ergodic measures
论文作者
论文摘要
在本文中，证明，如果最小系统具有其序列熵的特性，则对所有序列都均匀地界定了界限，那么它仅具有有限的许多ergodic措施，并且几乎是有限的，即其最大等效因素的一个扩展。该结果是作为一般标准的应用获得的，该标准指出，如果最小的系统几乎是其最大等效因素的一个延伸，并且对于某些$ k \ ge 2 $的无限独立$ k $，那么它只有有限的许多奇特的措施。
In this paper it is proved that if a minimal system has the property that its sequence entropy is uniformly bounded for all sequences, then it has only finitely many ergodic measures and is an almost finite to one extension of its maximal equicontinuous factor. This result is obtained as an application of a general criteria which states that if a minimal system is an almost finite to one extension of its maximal equicontinuous factor and has no infinite independent sets of length $k$ for some $k\ge 2$, then it has only finitely many ergodic measures.
