On jointly transitive commuting minimal homeomorphisms

Eli Glasner

On jointly transitive commuting minimal homeomorphisms

Dynamical Systems 2026-07-06 v1

Authors: Eli Glasner

Abstract

In analogy with ergodic theory, we introduce the notions of joint topological transitivity and joint minimality for commuting minimal homeomorphisms on a compact metric space $X$ . We prove an analogue of the Berend--Bergelson theorem for the first notion and investigate to what extent this theorem holds for the second.

Cite

@article{arxiv.2607.05161,
  title  = {On jointly transitive commuting minimal homeomorphisms},
  author = {Eli Glasner},
  journal= {arXiv preprint arXiv:2607.05161},
  year   = {2026}
}