Almost automorphic and bijective factors of substitution shifts
Abstract
In this article we completely characterise constant length substitution shifts which have an almost automorphic factor, or which have a bijective substitution factor. Our approach is algebraic: we study these dynamical properties in terms of a finite semigroup defined by the substitution. We characterise the existence of almost automorphic factors in terms of Green's R-relation, and the existence of bijective factors in terms of Green's L-relation. Our results are constructive.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2023
- DOI:
- 10.48550/arXiv.2307.01787
- arXiv:
- arXiv:2307.01787
- Bibcode:
- 2023arXiv230701787B
- Keywords:
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- Mathematics - Dynamical Systems;
- 37B02;
- 37B10;
- 37B52;
- 20M10;
- 20M35
- E-Print:
- 36 pages