幂零群上的乘法元胞自动机：结构、熵和渐近性
Multiplicative Cellular Automata on Nilpotent Groups: Structure, Entropy, and Asymptotics
摘要：
如果M是幺半群（例如格Z^D），G是有限（非阿贝尔）群，则G^M是紧群;“乘法细胞自动机”（MCA）是一个连续变换F：G^M-->G^M，它与所有移位映射交换，并且其中附近的坐标使用G的乘法运算组合。我们刻画了MCA是G^M的群自同态的条件，证明了G^M上的MCA继承了G^M的结构的自然结构理论。我们应用这一结构理论计算了MCA的可测熵，并研究了初始测度对Haar测度的收敛性。
英文摘要：
If M is a monoid (e.g. the lattice Z^D), and G is a finite (nonabelian) group, then G^M is a compact group; a `multiplicative cellular automaton' (MCA) is a continuous transformation F:G^M-->G^M which commutes with all shift maps, and where nearby coordinates are combined using the multiplication operation of G. We characterize when MCA are group endomorphisms of G^M, and show that MCA on G^M inherit a natural structure theory from the structure of G. We apply this structure theory to compute the measurable entropy of MCA, and to study convergence of initial measures to Haar measure.
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