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The Ellis semigroup of certain constant-length substitutions
- Source :
- Ergodic Theory and Dynamical Systems. 41:935-960
- Publication Year :
- 2019
- Publisher :
- Cambridge University Press (CUP), 2019.
-
Abstract
- In this article, we calculate the Ellis semigroup of a certain class of constant-length substitutions. This generalizes a result of Haddad and Johnson [IP cluster points, idempotents, and recurrent sequences. Topology Proc.22 (1997) 213–226] from the binary case to substitutions over arbitrarily large finite alphabets. Moreover, we provide a class of counterexamples to one of the propositions in their paper, which is central to the proof of their main theorem. We give an alternative approach to their result, which centers on the properties of the Ellis semigroup. To do this, we also show a new way to construct an almost automorphic–isometric tower to the maximal equicontinuous factor of these systems, which gives a more particular approach than the one given by Dekking [The spectrum of dynamical systems arising from substitutions of constant length. Z. Wahrscheinlichkeitstheor. Verw. Geb.41(3) (1977/78) 221–239].
- Subjects :
- medicine.medical_specialty
Dynamical systems theory
Semigroup
Applied Mathematics
General Mathematics
010102 general mathematics
Spectrum (functional analysis)
Symbolic dynamics
Topological dynamics
Equicontinuity
01 natural sciences
010101 applied mathematics
Combinatorics
medicine
0101 mathematics
Constant (mathematics)
Mathematics
Counterexample
Subjects
Details
- ISSN :
- 14694417 and 01433857
- Volume :
- 41
- Database :
- OpenAIRE
- Journal :
- Ergodic Theory and Dynamical Systems
- Accession number :
- edsair.doi...........6001161af6b8fbb23048d9ae8f69bc6b