| Title: |
Substitutions on compact alphabets |
| Authors: |
Mañibo, Neil; Walton, James J.; Rust, Dan |
| Publisher Information: |
Wiley |
| Publication Year: |
2025 |
| Collection: |
University of Nottingham: Repository@Nottingham |
| Subject Terms: |
substitutions; infinite alphabets; positive operators; quasi-compactness; unique ergodicity |
| Description: |
We develop a systematic approach to continuous substitutions on compact Hausdorff alphabets. Focussing on implications of irreducibility and primitivity, we highlight important features of the topological dynamics of their (generalised) subshifts. We then reframe questions from ergodic theory in terms of spectral properties of a corresponding substitution operator. This requires an extension of standard Perron-Frobenius theory to the setting of Banach lattices. As an application, we identify computable criteria that guarantee quasi-compactness of the substitution operator. This allows unique ergodicity to be verified for several classes of examples. For instance, it follows that every primitive and constant length substitution on an alphabet with an isolated point is uniquely ergodic, a result which fails when there are no isolated points. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
https://nottingham-repository.worktribe.com/output/45856375; Journal of the London Mathematical Society; Volume 111; Issue 3 |
| DOI: |
10.1112/jlms.70123 |
| Availability: |
https://doi.org/10.1112/jlms.70123; https://nottingham-repository.worktribe.com/file/45856375/1/Substitutions%20on%20compact%20alphabets; https://nottingham-repository.worktribe.com/output/45856375 |
| Rights: |
openAccess |
| Accession Number: |
edsbas.ED06DDC4 |
| Database: |
BASE |