On topological rank of factors of Cantor minimal systems
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 to...
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| Veröffentlicht in: | Ergodic theory and dynamical systems 2022-09, Vol.42 (9), p.2866-2889 |
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| container_title | Ergodic theory and dynamical systems |
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| creator | GOLESTANI, NASSER HOSSEINI, MARYAM |
| description | 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. |
| doi_str_mv | 10.1017/etds.2021.62 |
| format | Article |
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| subjects | Algebra Apexes Dynamical systems Mathematics Original Article Topology |
| title | On topological rank of factors of Cantor minimal systems |
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