维数大于零的有效动力系统与有限型子移位（SFTs）的因子
Effective dynamical systems beyond dimension zero and factors of SFTs
AI总结：
该研究借助可计算分析定义一般动力系统的有效性，证明有限生成递归表现群的有效动力系统是康托空间有效闭集上可计算作用的拓扑因子，并将模拟结果推广至零维空间外，指出一大类群的诸多自然作用是有限型子移位的拓扑因子。
摘要：
我们借助可计算分析工具，为一般动力系统提出了一种有效性概念：若任意空间上的群作用的拓扑共轭类中包含一个可计算代表元，则该动力系统是有效的。多数常见的自然系统都满足此有效性，包括部分群旋转、环面仿射作用以及有限表现代数作用。我们证明，对于有限生成且递归表现的群，每个有效动力系统都是康托空间的一个有效闭子集上可计算作用的拓扑因子。随后我们应用该结果，将现有文献中的模拟结果推广至零维空间之外。特别地，我们证明对于一大类群，这类自然作用中有许多都是有限型子移位（subshifts of finite type）的拓扑因子。
英文摘要：
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural systems one can think of are effective in this sense, including some group rotations, affine actions on the torus and finitely presented algebraic actions. We show that for finitely generated and recursively presented groups, every effective dynamical system is the topological factor of a computable action on an effectively closed subset of the Cantor space. We then apply this result to extend the simulation results available in the literature beyond zero-dimensional spaces. In particular, we show that for a large class of groups, many of these natural actions are topological factors of subshifts of finite type.
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