On Topological Rank of Factors of Cantor Minimal Systems

Abstract

A Cantor minimal system is of finite topological rank if it has a Bratteli-Vershik representation whose number of vertices per level is uniformly bounded. We prove that if the topological rank of a minimal dynamical system on a Cantor set is finite then all its minimal Cantor factors have finite topological rank as well. This gives an affirmative answer to a question posed by Donoso, Durand, Maass, and Petite.

20 pages

References in corpus (1)

• Symbolic factors of $\mathcal{S}$-adic subshifts of finite alphabet rank

Cited by in corpus (2)

• Symbolic factors of $\mathcal{S}$-adic subshifts of finite alphabet rank
• Subshifts of finite symbolic rank