English

Finite-to-one equivariant maps and mean dimension

Dynamical Systems 2023-12-11 v1

Abstract

We show that a minimal dynamical system (X,Z)(X,\mathbb{Z}) on a compact metric XX with mdimX=dX=d admits for every natural k>dk>d an equivariant map to the shift ([0,1]k)Z([0,1]^k)^{\mathbb{Z}} such that each fiber of this map contains at most [k/(kd)]k/(kd)[k/(k-d)]k/(k-d) points.

Keywords

Cite

@article{arxiv.2312.04689,
  title  = {Finite-to-one equivariant maps and mean dimension},
  author = {Michael Levin},
  journal= {arXiv preprint arXiv:2312.04689},
  year   = {2023}
}
R2 v1 2026-06-28T13:44:32.507Z