论文标题
详细的细胞自动机熵
Rescaled entropy of cellular automata
论文作者
论文摘要
对于具有D $ \ ge $ 1的d维蜂窝自动机，我们引入了一个重新筛选的熵，该熵通过概括以前的方法来估计熵在小尺度上的增长率[1，9]。我们还定义了Lyapunov指数的概念，并证明了[16，15]中d = 1的不平等现象。最后，我们将熵公式概括为一维置换性细胞自动机[18]，以更高尺寸的重新熵。最后的结果扩展了Shinoda和Tsukamoto的最新作品[17]，以处理二维符号动力学的度量平均维度。
For a d-dimensional cellular automaton with d $\ge$ 1 we introduce a rescaled entropy which estimates the growth rate of the entropy at small scales by generalizing previous approaches [1, 9]. We also define a notion of Lyapunov exponent and proves a Ruelle inequality as already established for d = 1 in [16, 15]. Finally we generalize the entropy formula for 1-dimensional permutative cellular automata [18] to the rescaled entropy in higher dimensions. This last result extends recent works [17] of Shinoda and Tsukamoto dealing with the metric mean dimensions of two-dimensional symbolic dynamics.
