标题： 渐近性，自同构群和强轨道等价 显示英文标题

标题： Asymptoticity, automorphism groups and strong orbit equivalence

摘要： 对于任意的强轨道等价类和任何有限、可数或连续的基数，我们证明了在这个给定的类中存在一个最小子移位，其渐近成分的数量恰好是给定的基数。 对于有限或可数的情况，我们明确构造了这类例子，使用了$\mathcal{S}$-adic 子移位。 我们通过证明任何具有可数个渐近成分的拓扑动力系统具有零拓扑熵，得出了不可数情况。 我们还构造了仅有一个渐近类但次指数词复杂度任意高的系统。 由此得出结论，在任何强轨道等价类中，都存在一个子移位，其自同构群同构于$\mathbb{Z}$。 显示英文摘要

摘要： Given any strong orbit equivalence class of minimal Cantor systems and any cardinal number that is finite, countable, or the continuum, we show that there exists a minimal subshift within the given class whose number of asymptotic components is exactly the given cardinal. For finite or countable ones, we explicitly construct such examples using $\mathcal{S}$-adic subshifts. We derived the uncountable case by showing that any topological dynamical system with countably many asymptotic components has zero topological entropy. We also construct systems with arbitrarily high subexponential word complexity with only one asymptotic class. We deduce that within any strong orbit equivalence class, there exists a subshift whose automorphism group is isomorphic to $\mathbb{Z}$.