论文标题
强轨道等效性和超线性复杂性
Strong Orbit Equivalence and Superlinear Complexity
论文作者
论文摘要
我们表明，在任何强轨道等效类别中，都有最小的乘坐乘坐，其任意较低的超线性复杂性。 This is done by proving that for any simple dimension group with unit $(G,G^+,u)$ and any sequence of positive numbers $(p_n)_{n\in\mathbb{N}}$ such that $\lim n/p_n=0$, there exist a minimal subshift whose dimension group is order isomorphic to $(G,G^+,u)$ and whose complexity function grows slower than $ p_n $。结果，我们会发现任何Choquet单纯形都可以实现为最小的Toeplitz subshift的一组不变度的度量，其复杂性的增长比$ p_n $慢。
We show that within any strong orbit equivalent class, there exist minimal subshifts with arbitrarily low superlinear complexity. This is done by proving that for any simple dimension group with unit $(G,G^+,u)$ and any sequence of positive numbers $(p_n)_{n\in\mathbb{N}}$ such that $\lim n/p_n=0$, there exist a minimal subshift whose dimension group is order isomorphic to $(G,G^+,u)$ and whose complexity function grows slower than $p_n$. As a consequence, we get that any Choquet simplex can be realized as the set of invariant measures of a minimal Toeplitz subshift whose complexity grows slower than $p_n$.
