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Mathematics > Dynamical Systems

arXiv:2206.00333 (math)
[Submitted on 1 Jun 2022 (v1), last revised 6 Nov 2024 (this version, v3)]

Title:$\mathcal{S}$-adic characterization of minimal dendric shifts

Authors:France Gheeraert, Julien Leroy
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Abstract:Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian shifts, Arnoux-Rauzy shifts and codings of interval exchange transformations. It is known that any minimal dendric shift has a primitive $\mathcal{S}$-adic representation where the morphisms in $\mathcal{S}$ are positive tame automorphisms of the free group generated by the alphabet. In this paper we give an $\mathcal{S}$-adic characterization of this family by means of two finite graphs. As an application, we are able to decide whether a shift space generated by a uniformly recurrent morphic word is (eventually) dendric.
Comments: 28 pages
Subjects: Dynamical Systems (math.DS); Discrete Mathematics (cs.DM)
MSC classes: 68R15, 37B10
Cite as: arXiv:2206.00333 [math.DS]
  (or arXiv:2206.00333v3 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.2206.00333

Submission history

From: France Gheeraert [view email]
[v1] Wed, 1 Jun 2022 08:50:02 UTC (31 KB)
[v2] Thu, 22 Feb 2024 15:25:47 UTC (36 KB)
[v3] Wed, 6 Nov 2024 14:33:24 UTC (36 KB)
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