Catalan numbers as discrepancies for a family of substitutions on infinite alphabets

D Frettlöh, A Garber, N Mañibo - Indagationes Mathematicae, 2024 - Elsevier
In this work, we consider a class of substitutions on infinite alphabets and show that they
exhibit a growth behaviour which is impossible for substitutions on finite alphabets. While for …

Bratteli diagrams in Borel dynamics

S Bezuglyi, PET Jorgensen, O Karpel… - Groups, Geometry, and …, 2025 - ems.press
Bratteli–Vershik models have been very successfully applied to the study of various
dynamical systems, in particular, in Cantor dynamics. In this paper, we study dynamics on …

[PDF][PDF] Aperiodic order and singular spectra

P Gohlke - 2021 - d-nb.info
A central motive of this thesis is the study of configurations with aperiodic order. Here, a
configuration may refer to a bi-infinite sequence of symbols, a tiling of the plane or a …

Inverse limit method for generalized Bratteli diagrams and invariant measures

S Bezuglyi, O Karpel, J Kwiatkowski, M Wata - arXiv preprint arXiv …, 2024 - arxiv.org
Generalized Bratteli diagrams with a countable set of vertices in every level are models for
aperiodic Borel automorphisms. This paper is devoted to the description of all ergodic …

Measures and dynamics on Pascal-Bratteli diagrams

S Bezuglyi, A Dudko, O Karpel - arXiv preprint arXiv:2411.06280, 2024 - arxiv.org
We introduce stationary generalized Bratteli diagrams $ B $ which are represented as the
union of countably many classical Pascal-Bratteli diagrams. We describe all ergodic …

[PDF][PDF] Dynamics on the path space of generalized Bratteli diagrams

S Bezuglyi, PET Jorgensen, O Karpel, S Sanadhya - ArXiv. org, 2022 - academia.edu
Bratteli-Vershik models have been very successfully applied to the study of various
dynamical systems, in particular, in Cantor dynamics. In this paper, we study dynamics on …

Spectral properties of substitutions on compact alphabets

N Mañibo, D Rust, JJ Walton - Bulletin of the London …, 2023 - Wiley Online Library
We consider substitutions on compact alphabets and provide sufficient conditions for the
diffraction to be pure point, absolutely continuous and singular continuous. This allows one …

A smoking cessation smartphone app that delivers real-time 'context aware'behavioural support: the Quit Sense feasibility RCT

F Naughton, A Hope, C Siegele-Brown… - Public Health …, 2024 - kclpure.kcl.ac.uk
Background: During a quit attempt, cues from a smoker's environment are a major cause of
brief smoking lapses, which increase the risk of relapse. Quit Sense is a theory-guided Just …