InforLorV4, Main, Exploration, bibRecord, 001007

Structuring multi-dimensional subshifts

Identifieur interne : 001007 ( Main/Exploration ); précédent : 001006; suivant : 001008

Structuring multi-dimensional subshifts

Auteurs : Alexis Ballier [Chili] ; Emmanuel Jeandel [France]

Source :

RBID : Hal:hal-00868899

Abstract

We study two relations on multi-dimensional subshifts: A pre-order based on the patterns configurations contain and the Cantor-Bendixson rank. We exhibit several structural properties of two-dimensional subshifts: We characterize the simplest aperiodic configurations in countable SFTs, we give a combinatorial characterization of uncountable subshifts, we prove that there always exists configurations without any periodicity but that have the simplest possible combinatorics in countable SFTs. Finally, we prove that some Cantor-Bendixson ranks are impossible for countable SFTs, leaving only a few unknown cases.

Url:

https://hal.inria.fr/hal-00868899

Affiliations:

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Le document en format XML

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<front><div type="abstract" xml:lang="en">We study two relations on multi-dimensional subshifts: A pre-order based on the patterns configurations contain and the Cantor-Bendixson rank. We exhibit several structural properties of two-dimensional subshifts: We characterize the simplest aperiodic configurations in countable SFTs, we give a combinatorial characterization of uncountable subshifts, we prove that there always exists configurations without any periodicity but that have the simplest possible combinatorics in countable SFTs. Finally, we prove that some Cantor-Bendixson ranks are impossible for countable SFTs, leaving only a few unknown cases.</div>
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Structuring multi-dimensional subshifts

Structuring multi-dimensional subshifts

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Abstract

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