标题： 符号频率在满射细胞自动机中 显示英文标题

标题： Symbol Frequencies in Surjective Cellular Automata

摘要： 我们研究了在满射元胞自动机迭代下概率测度的行为。我们以否定的方式回答了以下问题：如果初始测度是遍历的且具有全支集，那么测度序列的所有弱*极限点是否也具有全支集？我们的解答中的初始测度不是一个乘积测度，在这种情况下该问题仍然是开放的。为此，我们提出了一种工具用于研究满射元胞自动机前像中符号频率的问题，并证明了一些基本结果。然而，我们表明，仅靠这一工具不足以正面解决更为严格的问题。 显示英文摘要

摘要： We study the behavior of probability measures under iteration of a surjective cellular automaton. We solve the following question in the negative: if the initial measure is ergodic and has full support, do all weak-* limit points of the sequence of measures have full support as well? The initial measure of our solution is not a product measure, and in this case the question remains open. To this end, we present a tool for studying the frequencies of symbols in preimages of surjective cellular automata, and prove some basic results about it. However, we show that by itself it is not enough to solve the stricter question in the positive.