论文标题
从理论上衡量最小单词复杂性的子迁移
Measure-Theoretically Mixing Subshifts of Minimal Word Complexity
论文作者
论文摘要
我们通过建立确切的单词复杂性来解决衡量理论动力学复杂性与符号复杂性之间关系的长期开放问题，在这种情况下，衡量理论强的混合体现出来： 对于每一个超级线性$ f：\ mathbb {n} \ to \ mathbb {n} $，即$ f（q）/q \ to \ infty $，存在一个subshift，将所有订单的概率概率与Word Complactity undersy概率$ P $ P $ P $（Q）/F（q）/f（q）/f（q）/f（q）/f（q）/f（q）/f（q）混合在一起。 对于单词复杂性$ p $的子缩影，即非useplineare，即$ \ liminf p（q）/q <\ infty $，每个ergodic概率度量都是部分刚性的。
We resolve a long-standing open question on the relationship between measure-theoretic dynamical complexity and symbolic complexity by establishing the exact word complexity at which measure-theoretic strong mixing manifests: For every superlinear $f : \mathbb{N} \to \mathbb{N}$, i.e. $f(q)/q \to \infty$, there exists a subshift admitting a (strongly) mixing of all orders probability measure with word complexity $p$ such that $p(q)/f(q) \to 0$. For a subshift with word complexity $p$ which is non-superlinear, i.e. $\liminf p(q)/q < \infty$, every ergodic probability measure is partially rigid.
