论文标题
粗空间，超滤器和动态系统
Coarse spaces, ultrafilters and dynamical systems
论文作者
论文摘要
对于粗大空间$（x，\ mathcal {e}）$，$ x^\ sharp $表示与平行关系的$ x $上的所有无限的超滤器集合：$ p || q $如果存在$ e \ in \ mathcal {e} $ in \ mathcal {e} $ in \ e [e [p] $ e [p] q $ q $ $ $ p \ $如果$（x，\ mathcal {e}）$是限制的，则存在$ x $的$ g $的组$ g $，使得粗体结构$ \ mathcal {e} $具有base $ \ \ {\ {（x，gx，gx）：x $ in x $ g \ in x $ g \ in f \}： \}。$我们调查和分析$（x，\ mathcal {e}）$，$ x^\ sharp $和动态系统$（g，x^\ sharp）$之间的相互作用。
For a coarse space $(X, \mathcal{E})$, $X^\sharp$ denotes the set of all unbounded ultrafilters on $X$ endowed with the parallelity relation: $p||q$ if there exists $E \in \mathcal{E} $ such that $ E[P]\in q $ for each $P\in p$. If $(X, \mathcal{E})$ is finitary then there exists a group $G $ of permutations of $X$ such that the coarse structure $\mathcal{E}$ has the base $\{\{ (x,gx): x\in X$, $g\in F\}: F\in [G]^{<ω}, \ id \in F \}.$ We survey and analyze interplays between $(X, \mathcal{E})$, $X^\sharp$ and the dynamical system $(G, X^\sharp)$.
