AI 中文总结
该研究给出置换滑动块码提升子转移时保持极小性与唯一遍历性的判据，通过示例构造严格遍历有限到一扩张，还发现其提升的极小子转移可能非唯一遍历的特殊现象。
AI 中文摘要
Hedlund意义下的置换滑动块码可生成子转移的有限到一扩张。我们提供了该“提升过程”保持极小性与唯一遍历性的判据。通过若干自然示例族阐释这些发现，用于获得置换子转移（包括斐波那契、 tribonacci、银均值及贵族均值置换）的严格遍历有限到一扩张。我们进一步研究置换滑动块码与Toeplitz流的相互作用，特别找到示例表明，严格遍历子转移的置换提升可为极小但非唯一遍历，此现象对本原置换子转移不会出现。
英文摘要
Permutative sliding block codes - in the sense of Hedlund - give rise to finite-to- one extensions of subshifts. We provide criteria under which minimality and unique ergodicity are preserved by this 'lifting procedure'. These findings are illustrated by means of some nat- ural example families, which we use to obtain strictly ergodic finite-to-one extensions of sub- stitution subshifts (including the case of Fibonacci, Tribonacci, silver mean and noble means substitutions). We further study the interplay between permutative sliding block codes and Toeplitz flows. In particular, we find examples which demonstrate that a permutative lift of a strictly ergodic subshift may be minimal, but not uniquely ergodic - a phenomenon which cannot occur for primitive substitution subshifts.
