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Pré-Publication, Document De Travail Année : 2024

Substreetutions and more on trees

Résumé

We define a notion of substitution on colored binary trees that we call substreetution. We show that a fixed point by a substreetution may be (or not) almost periodic, thus the closure of the orbit under $\mathbb{F}_2^+$-action may (or not) be minimal. We study one special example: we show that it belongs to the minimal case and that the number of preimages in the minimal set increases just exponentially fast, whereas it could be expected a super-exponential growth. We also give examples of periodic trees without invariant measure on their orbit. We use our construction to get quasi-periodic colored tilings of the hyperbolic disk.

Dates et versions

hal-04442982 , version 1 (07-02-2024)

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A. Baraviera, Renaud Leplaideur. Substreetutions and more on trees. 2024. ⟨hal-04442982⟩
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