Topological Dynamics indexed by words
Topological Dynamics indexed by words
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DOI：
10.1016/j.topol.2011.05.041
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发表时间：
2011-01
期刊：
影响因子：
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通讯作者：
V. Farmaki;Andreas Koutsogiannis
中科院分区：
文献类型：
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作者：
V. Farmaki;Andreas Koutsogiannis
从作者最近建立的由固定序列支配的无限字母表上的词的组合划分定理出发，证明了由这类词标引的拓扑动力系统的递推结果。通过这种方法，我们将Furstenberg和Weiss发展的自然数标度动力系统的经典理论推广到词标度系统。此外，将这一理论应用于可表示为词的半群索引的拓扑系统，得到了类似的递推结果。
Starting with a combinatorial partition theorem for words over an infinite alphabet dominated by a fixed sequence, established recently by the authors, we prove recurrence results for topological dynamical systems indexed by such words. In this way we extend the classical theory developed by Furstenberg and Weiss of dynamical systems indexed by the natural numbers to systems indexed by words. Moreover, applying this theory to topological systems indexed by semigroups that can be represented as words we get analogous recurrence results for such systems.