Geodesic
Substitution tilings with transcendental inflation factor
Discrete analysis (2024) Cet article a éte moissonné depuis la source Scholastica

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For any $λ>2$, we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor $λ$. In particular, we obtain the first class of examples of substitutive systems with transcendental inflation factors that possess usual dynamical properties enjoyed by primitive substitutions on finite alphabets. We show that both the associated subshift and tiling dynamical systems are strictly ergodic, which is related to the quasicompactness of the underlying substitution operator. We also provide an explicit substitution with transcendental inflation factor $λ$.
Publié le : 
@article{DAS_2024_a10,
     author = {Dirk Frettl\"oh and Alexey Garber and Neil Ma\~nibo},
     title = {Substitution tilings with transcendental inflation factor},
     journal = {Discrete analysis},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2024_a10/}
}
TY  - JOUR
AU  - Dirk Frettlöh
AU  - Alexey Garber
AU  - Neil Mañibo
TI  - Substitution tilings with transcendental inflation factor
JO  - Discrete analysis
PY  - 2024
UR  - http://geodesic.mathdoc.fr/item/DAS_2024_a10/
LA  - en
ID  - DAS_2024_a10
ER  - 
%0 Journal Article
%A Dirk Frettlöh
%A Alexey Garber
%A Neil Mañibo
%T Substitution tilings with transcendental inflation factor
%J Discrete analysis
%D 2024
%U http://geodesic.mathdoc.fr/item/DAS_2024_a10/
%G en
%F DAS_2024_a10
Dirk Frettlöh; Alexey Garber; Neil Mañibo. Substitution tilings with transcendental inflation factor. Discrete analysis (2024). http://geodesic.mathdoc.fr/item/DAS_2024_a10/