标题： 符号频率在满射胞状自动机中 显示英文标题

标题： Symbol Frequencies in Surjective Cellular Automata

摘要： 我们研究了概率测度在满射元胞自动机迭代下的行为。 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来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。 % 我们知道它们是非平凡的吗？ :P 然而，我们表明，仅靠这个工具不足以正面解决更严格的问题。 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. % do we know they are nontrivial? :P However, we show that by itself it is not enough to solve the stricter question in the positive.