论文标题
关于双重表面和应用
On Dual surjunctivity and applications
论文作者
论文摘要
我们探索了Capobianco，Kari和Taati最近引入的Gottschalk猜想的双重版本，以及一般而言双重表面性的概念。我们表明，双重表面群体满足了Kaplansky对所有积极特征领域的直接有限猜想。通过量化细胞自动机的注入性和解释后的概念，我们表明，在注射式蜂窝自动机下进行的完整拓扑移动的图像是以定量方式的有限类型的subshift。此外，我们表明，在基本等效性下和某些半领产品下（使用Arzhantseva和Gal的思想，后者的思想），双表面群体在超副作用下关闭。它们在标记组的空间中形成了一个封闭的子集，完全残留的双重表面群是双表面性的，等等。我们还考虑采用Chung and Li的结果，用于某些广泛的代数作用，即对某些广泛的代数作用，即对更通用的动力学系统进行双重表面系统。
We explore the dual version of Gottschalk's conjecture recently introduced by Capobianco, Kari, and Taati, and the notion of dual surjunctivity in general. We show that dual surjunctive groups satisfy Kaplansky's direct finiteness conjecture for all fields of positive characteristic. By quantifying the notions of injectivity and post-surjectivity for cellular automata, we show that the image of the full topological shift under an injective cellular automaton is a subshift of finite type in a quantitative way. Moreover we show that dual surjunctive groups are closed under ultraproducts, under elementary equivalence, and under certain semidirect products (using the ideas of Arzhantseva and Gal for the latter); they form a closed subset in the space of marked groups, fully residually dual surjunctive groups are dual surjunctive, etc. We also consider dual surjunctive systems for more general dynamical systems, namely for certain expansive algebraic actions, employing results of Chung and Li.
