论文标题
同构的度量平均维度的水平集的密度
Density of the level sets of the metric mean dimension for homeomorphisms
论文作者
论文摘要
令$ n $为$ n $ dimensional compact riemannian歧管，带有$ n \ geq 2 $。在本文中，我们证明，对于[0，n] $中的任何$α\，由$ n $上的同构的集合组成的集合，$ n $等于$α$，$ \ text {hom}（hom}（n）$，等于$α$。更普遍地，给定$α，β\在[0，n] $中，$α\ leqβ$，我们显示的集合由$ n $的同构型组成，较低的度量平均尺寸等于$α$，高等于$α$，上的公制尺寸等于$β$，等于$β$在$ \ text {hom}（n hom）中是密集的。此外，我们还提供证据，表明等同于$ n $的同构同构的集合在$ \ text {hom}（n）$中是残留的。
Let $N$ be an $n$-dimensional compact riemannian manifold, with $n\geq 2$. In this paper, we prove that for any $α\in [0,n]$, the set consisting of homeomorphisms on $N$ with lower and upper metric mean dimensions equal to $α$ is dense in $\text{Hom}(N)$. More generally, given $α,β\in [0,n]$, with $α\leq β$, we show the set consisting of homeomorphisms on $N$ with lower metric mean dimension equal to $α$ and upper metric mean dimension equal to $β$ is dense in $\text{Hom}(N)$. Furthermore, we also give a proof that the set of homeomorphisms with upper metric mean dimension equal to $n$ is residual in $\text{Hom}(N)$.
