Generic homeomorphisms have full metric mean dimension
Dynamical Systems
2023-06-22 v1 General Topology
Geometric Topology
Abstract
We prove that the upper metric mean dimension of -generic homeomorphisms, acting on a compact smooth boundaryless manifold with dimension greater than one, coincides with the dimension of the manifold. In the case of continuous interval maps we also show that each level set for the metric mean dimension is -dense in the space of continuous endomorphisms of with the uniform topology.
Cite
@article{arxiv.1910.07376,
title = {Generic homeomorphisms have full metric mean dimension},
author = {Maria Carvalho and Fagner B. Rodrigues and Paulo Varandas},
journal= {arXiv preprint arXiv:1910.07376},
year = {2023}
}