论文标题
将腰部不等式应用于熵和平均维度
Application of waist inequality to entropy and mean dimension
论文作者
论文摘要
腰部不平等是几何和拓扑的根本不平等。我们将其应用于熵的研究和动态系统的平均维度。我们考虑动态系统之间的均值连续图，并假设域的平均维度大于目标的平均维度。我们表现出几种情况，这些情况必定具有正性度量平均维度。这项研究对拓扑条件熵的理论产生了有趣的后果。特别是，它阐明了Lindenstrauss和Weiss的著名结果，介绍了Hilbert Cube转移中不可嵌入的最小动态系统。
Waist inequality is a fundamental inequality in geometry and topology. We apply it to the study of entropy and mean dimension of dynamical systems. We consider equivariant continuous maps between dynamical systems and assume that the mean dimension of the domain is larger than the mean dimension of the target. We exhibit several situations for which the maps necessarily have positive conditional metric mean dimension. This study has interesting consequences to the theory of topological conditional entropy. In particular it sheds new light on a celebrated result of Lindenstrauss and Weiss about minimal dynamical systems non-embeddable in the shift on the Hilbert cube.
