Thursday, August 24, 2023 - 16:10 in V5-148
Factors of substitutive shift spaces and the column semigroup
A talk in the Micro-symposium on Substitution Dynamical Systems series by
Álvaro Bustos from Pontificia Universidad Católica de Chile, Chile
| Abstract: |
We discuss algebraic criteria to determine whether a given constant-length substitution has a substitutive factor with specific properties of dynamical interest, namely being either almost automorphic or bijective. The key tool for this analysis is the column semigroup $S(\theta)$ associated to the substitution, which, while not a conjugacy invariant, gives plenty of information about the structure of the points of the associated shift space. By choosing an appropriate presentation of the shift space $X(\theta)$ (that is, finding an adequate substitution η for which $X(\eta) \cong X(\theta))$, this leads to a complete algorithmic criterion for the existence of these factors via the use of standard tools in the theory of substitutions such as collaring.
Within the CRC this talk is associated to the project(s): A6 |
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