拓扑可测动力学的族独立性
Family-independence for topological and measurable dynamics
摘要：
对于族F（Z_+的子集的集合），定义了F-独立性的概念，它既适用于拓扑动力学（t.d.s.）和可测量动力学（m.d.s.）。证明了不存在非平凡的{syndetic}-独立的m.d.s.;医学博士是{正密度}独立的当且仅当它具有完全正熵;和一个m.d.s.是弱混合的当且仅当它是{IP}-独立的。对于一个t.d. s。证明了不存在非平凡的极小{syndetic}-独立系统，并给出了一个t.d.s.是弱混合的当且仅当它是{IP}-独立的。此外，构造了一个非平凡的邻近拓扑K系，并给出了极小拓扑K蕴涵强混合的拓扑证明。
英文摘要：
For a family F (a collection of subsets of Z_+), the notion of F-independence is defined both for topological dynamics (t.d.s.) and measurable dynamics (m.d.s.). It is shown that there is no non-trivial {syndetic}-independent m.d.s.; a m.d.s. is {positive-density}-independent if and only if it has completely positive entropy; and a m.d.s. is weakly mixing if and only if it is {IP}-independent. For a t.d.s. it is proved that there is no non-trivial minimal {syndetic}-independent system; a t.d.s. is weakly mixing if and only if it is {IP}-independent. Moreover, a non-trivial proximal topological K system is constructed, and a topological proof of the fact that minimal topological K implies strong mixing is presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
