AI 中文总结
该研究刻画了零系统与等度连续系统的极大模式复杂性等价条件，构造了两类特殊传递非极小零系统，解决了多项式极大模式增长及传递非极小零系统结构领域的若干长期公开问题。
AI 中文摘要
紧可度量化系统若沿每一个时间序列的拓扑序列熵均消失，则称其为零系统。我们证明，对任意有限开覆盖，零性等价于多项式极大模式复杂性，而等度连续性等价于次线性极大模式复杂性。第一个刻画是通过在每个正尺度下的有限胖击碎性及轨道距离类的多项式经验覆盖得到的。我们还构造了具有极小情形中排除性质的传递非极小零系统：一个是一致刚性且具有两个不动点，另一个是双散射的。这些结果解决了文献中关于多项式极大模式增长及传递非极小零系统结构的几个长期悬而未决的公开问题。
英文摘要
A compact metrizable system is null if its topological sequence entropy vanishes along every sequence of times. We prove that nullness is equivalent to polynomial maximal pattern complexity for every finite open cover, while equicontinuity is equivalent to sublinear maximal pattern complexity. The first characterization is obtained from finite fat-shattering at every positive scale and polynomial empirical covering of orbit-distance classes. We also construct transitive nonminimal null systems with properties excluded in the minimal setting: one is uniformly rigid and has two fixed points, and another is two-scattering. These results settle several long-standing open problems from the literature on polynomial maximal pattern growth and on the structure of transitive nonminimal null systems.
Comments34 pages
