Multi-dimensional symbolic dynamical systems
Multi-dimensional symbolic dynamical systems
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多维符号动力系统
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
K. Schmidt
中科院分区：
文献类型：
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作者：
K. Schmidt
本文的目的是指出从有限型X <$A <$d的经典移位到有限型X <$A <$d的多维移位（d ≥ 2，其中A是有限字母表）的过渡中出现的一些现象。我们讨论了某些多维移位的刚性性质，如出现意想不到的内在代数结构或同构和不变测度的稀缺性。最后一节集中于有限或不可数字母的群移位，以及在后一种情况下这种移位的符号表示。
The purpose of this note is to point out some of the phenomena which arise in the transition from classical shifts of finite type X ⊂ A ℤ to multi-dimensional shifts of finite type X ⊂ A ℤ d, d ≥ 2, where A is a finite alphabet. We discuss rigidity properties of certain multi-dimensional shifts, such as the appearance of an unexpected intrinsic algebraic structure or the scarcity of isomorphisms and invariant measures. The final section concentrates on group shifts with finite or uncountable alphabets, and with the symbolic representation of such shifts in the latter case.