Beyond substitutive dynamical systems: S-adic expansions

V Berthé, V Delecroix - arXiv preprint arXiv:1309.3960, 2013 - arxiv.org
An S-adic expansion of an infinite word is a way of writing it as the limit of an infinite product
of substitutions (ie, morphisms of a free monoid). Such a description is related to continued …

Recognizability for sequences of morphisms

V Berthé, W Steiner, JM Thuswaldner… - Ergodic theory and …, 2019 - cambridge.org
Recognizability for sequences of morphisms Page 1 Ergod. Th. & Dynam. Sys. (2019), 39,
2896–2931 doi:10.1017/etds.2017.144 c Cambridge University Press, 2018 Recognizability for …

Recognizability of morphisms

MP Béal, D Perrin, A Restivo - Ergodic Theory and Dynamical …, 2023 - cambridge.org
We investigate several questions related to the notion of recognizable morphism. The main
result is a new proof of Mossé's theorem and actually of a generalization to a more general …

About the domino problem for subshifts on groups

N Aubrun, S Barbieri, E Jeandel - Sequences, groups, and number theory, 2018 - Springer
From a classical point of view, the domino problem is the question of the existence of an
algorithm which can decide whether a finite set of square tiles with colored edges can tile …

Shift spaces on groups: computability and dynamics

SAB Lemp - 2017 - theses.hal.science
Shift spaces are sets of colorings of a group which avoid a set of forbidden patterns and are
endowed with a shift action. These spaces appear naturally as discrete versions of …

Coboundaries and eigenvalues of finitary S-adic systems

V Berthé, PC Bernales, R Yassawi - arXiv preprint arXiv:2202.07270, 2022 - arxiv.org
An S-adic system is a symbolic dynamical system generated by iterating an infinite
sequence of substitutions or morphisms, called a directive sequence. A finitary S-adic …

Quantified block gluing for multidimensional subshifts of finite type: Aperiodicity and entropy

S Gangloff, M Sablik - Journal d'Analyse Mathématique, 2021 - Springer
It is possible to extend the notion of block gluing for subshifts studied in [PS15] adding a gap
function which gives the distance which allows to concatenate two rectangular blocks of the …

Subshifts of Finite Type on Groups: Emptiness and Aperiodicity

N Bitar - 2024 - theses.hal.science
A subshift of finite type is a set of tilings of a group subject to a finite number of local
constraints, where the group acts by translation. In recent years, much progress has been …

[图书][B] Sequences, groups, and number theory

V Berthé, M Rigo - 2018 - Springer
This collaborative volume aims at presenting and developing recent trends at the interface
between the study of sequences, groups, and number theory, as the title may suggest. It is …

Quantified block gluing, aperiodicity and entropy of multidimensional SFT

S Gangloff, M Sablik - arXiv preprint arXiv:1706.01627, 2017 - arxiv.org
It is possible to define mixing properties for subshifts according to the intensity which allows
to concatenate two rectangular blocks. We study the interplay between this intensity and …