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Paper   IPM / M / 16942
School of Mathematics
  Title:   On topological rank of factors of Cantor minimal systems
1.  Nasser Golestani
2.  Maryam Hosseini
  Status:   To Appear
  Journal: Ergod. Th. & Dynam. Sys.
  Supported by:  IPM
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 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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