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. We also show that both the associated subshift and tiling dynamical systems are strictly ergodic, which is related to the quasicompactness of the underlying substitution operator.
Frettlöh, Dirk, Alexey Garber, and Neil Mañibo. "Substitution tilings with transcendental inflation factor." arXiv preprint arXiv:2208.01327 (2022).
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