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Paper IPM / M / 16634  


Abstract:  
A Cantor minimal system is of finite topological rank if it
has a BratteliVershik 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 in full
generality. As a consequence, we obtain the dichotomy of Downarowicz
and Maass for Cantor factors of finite rank Cantor minimal systems:
they are either odometers or subshifts.
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