论文标题
在可数的小组动作系统上进行阴影和混合
Shadowing and mixing on systems of countable group actions
论文作者
论文摘要
令$（x，g，φ）$为一个动态系统，其中$ x $是紧凑的hausdorff空间，而$ g $是一个可计数的离散组。我们研究了阴影属性并在子缩合和一般动力学系统之间进行混合。对于阴影属性，请修复一些有限的子集$ S \子集G $。我们证明，如果$ x $完全断开连接，则$φ$具有$ s $展示的属性，并且仅当$（x，g，φ）$与满足Mittag-Leffler条件的有限型类型的一系列偏移序列相反。另外，假设$ x $是公制空间（可能不是完全断开的），我们证明，如果$φ$具有$ s $ shad的属性，则$（x，g，φ）$是由一个因子映射的一系列有限型偏移序列的因素，几乎可以将pseudo-orbit的因子提起$ s $。 另一方面，让属性$ p $成为以下属性之一：传递性，最小，完全传递性，弱混合，混合和规范属性。我们证明，如果$ x $完全断开连接，则$φ$具有属性$ p $，并且仅当$（x，g，φ）$与属性$ p $组成的逆向系统的逆极限相连，该属性$ p $满足Mittag-Leffler条件。另外，对于公制空间（可能不是完全断开连接），如果属性$ p $不是最小或规范属性，我们证明$φ$当时具有属性$ p $，并且仅当$（x，g，φ）$是与属性$ p $ syage mittagg-lefffler条件相对限制的因素。
Let $(X,G,Φ)$ be a dynamical system, where $X$ is compact Hausdorff space, and $G$ is a countable discrete group. We investigate shadowing property and mixing between subshifts and general dynamical systems. For the shadowing property, fix some finite subset $S\subset G$. We prove that if $X$ is totally disconnected, then $Φ$ has $S$-shadowing property if and only if $(X,G,Φ)$ is conjugate to an inverse limit of a sequence of shifts of finite type which satisfies Mittag-Leffler condition. Also, suppose that $X$ is metric space (may be not totally disconnected), we prove that if $Φ$ has $S$-shadowing property, then $(X,G,Φ)$ is a factor of an inverse limit of a sequence of shifts of finite type by a factor map which almost lifts pseudo-orbit for $S$. On the other hand, let property $P$ be one of the following property: transitivity, minimal, totally transitivity, weakly mixing, mixing, and specification property. We prove that if $X$ is totally disconnected, then $Φ$ has property $P$ if and only if $(X,G,Φ)$ is conjugate to an inverse limit of an inverse system that consists of subshifts with property $P$ which satisfies Mittag-Leffler condition. Also, for the case of metric space (may be not totally disconnected), if property $P$ is not minimal or specification property, we prove that $Φ$ has property $P$ if and only if $(X,G,Φ)$ is a factor of an inverse limit of a sequence of subshifts with property $P$ which satisfies Mittag-Leffler condition.
