English

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 C0C^0-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 C0C^0-dense in the space of continuous endomorphisms of [0,1][0,1] with the uniform topology.

Keywords

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}
}
R2 v1 2026-06-23T11:45:28.524Z