Besicovitch 空间中细胞自动机的满射性
动力系统
2008-06-16 v3
摘要
Besicovitch 伪距离度量了两个函数取值不同的点集的相对大小；模去诱导等价关系后的商空间被赋予了一个自然度量。我们研究了细胞自动机在这种新拓扑下的行为，并表明在适当的附加假设下，它们保留了在通常乘积拓扑中所具有的某些性质；特别是，单射性仍然蕴含满射性。
引用
@article{arxiv.0705.0670,
title = {Surjunctivity for cellular automata in Besicovitch spaces},
author = {Silvio Capobianco},
journal= {arXiv preprint arXiv:0705.0670},
year = {2008}
}
备注
9 pages, no figures, LaTeX. Shortened, some definition changed, proof of main lemma changed accordingly. Almost as submitted to Journal of Cellular Automata for special issue dedicated to Automata 2007 conference proceedings. Exceptions: one major error corrected in definition of surjunctivity; adapted for use of the article document class