M. Coornaert

activity

20082026

most citedOn the density of periodic configurations in strongly irreducible subshifts

33 citations · 162 across the 31 of their papers we have counts for

collaborators

38 papers

math.DS2026

On surjunctive and injunctive subshifts of finite type

Tullio Ceccherini-Silberstein, Michel Coornaert, Ville Salo

A dynamical system is said to be surjunctive if every injective endomorphism of the system is surjective and it is said to be injunctive if every surjective endomorphism is injecti…

math.DS2025

A Garden of Eden theorem for Smale spaces

Tullio Ceccherini-Silberstein, Michel Coornaert

Given a dynamical system $(X, f)$ consisting of a compact metrizable space $X$ and a homeomorphism $f : X \to X$ , an endomorphism of $(X, f)$ is a continuous map of $X$ into its…

math.DS2025

Topological stability of semigroup actions and shadowing

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

We investigate expansiveness, topological stability, and shadowing for continuous actions of semigroups on compact Hausdorff spaces. We characterize semigroups for which all full s…

math.GR2024

Strongly sofic monoids, sofic topological entropy, and surjunctivity

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

We introduce the class of strongly sofic monoids. This class of monoids strictly contains the class of sofic groups and is a proper subclass of the class of sofic monoids. We defin…

math.RA2024

Stable finiteness of monoid algebras and surjunctivity

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

A monoid $M$ is said to be surjunctive if every injective cellular automaton with finite alphabet over $M$ is surjective. We show that monoid algebras of surjunctive monoids are st…

math.GR2023★ 1 cited

First-order model theory and Kaplansky's stable finiteness conjecture

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

Using algebraic geometry methods, the third author proved that the group ring of a surjunctive group with coefficients in a field is always stably finite. In other words, every gro…

math.DS2021★ 4 cited

Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity

Tullio Ceccherini-Silberstein, Michel Coornaert, Hanfeng Li

A dynamical system is a pair $(X, G)$ , where $X$ is a compact metrizable space and $G$ is a countable group acting by homeomorphisms of $X$ . An endomorphism of $(X, G)$ is a continuo…

math.DS2020★ 12 cited

On linear shifts of finite type and their endomorphisms

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

Let $G$ be a group and let $A$ be a finite-dimensional vector space over an arbitrary field $K$ . We study finiteness properties of linear subshifts $Σ \subset A^{G}$ and the dynamical…

math.DS2020★ 8 cited

Invariant sets and nilpotency of endomorphisms of algebraic sofic shifts

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

Let $G$ be a group and let $V$ be an algebraic variety over an algebraically closed field $K$ . Let $A$ denote the set of $K$ -points of $V$ . We introduce algebraic sofic subshifts $…

math.DS2019★ 10 cited

Expansive actions with specification on uniform spaces, topological entropy, and the Myhill property

Tullio Ceccherini-Silberstein, Michel Coornaert

We prove that every expansive continuous action with the weak specification property of an amenable group $G$ on a compact Hausdorff space $X$ has the Myhill property, i.e., every…

math.DS2018★ 14 cited

On the Garden of Eden theorem for endomorphisms of symbolic algebraic varieties

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

Let $G$ be an amenable group and let $X$ be an irreducible complete algebraic variety over an algebraically closed field $K$ . Let $A$ denote the set of $K$ -points of $X$ and let $τ…

math.DS2018★ 3 cited

Homoclinically expansive actions and a Garden of Eden theorem for harmonic models

Tullio Ceccherini-Silberstein, Michel Coornaert, Hanfeng Li

Let $Γ$ be a countable Abelian group and $f \in Z [Γ]$ , where $Z [Γ]$ denotes the integral group ring of $Γ$ . Consider the Pontryagin dual $X_{f}$ of the cyclic $Z [Γ]$ -module $\Z[Γ]…

math.AG2017

On injective endomorphisms of symbolic schemes

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung

Building on the seminal work of Gromov on endomorphisms of symbolic algebraic varieties [10], we introduce a notion of cellular automata over schemes which generalize affine algebr…

math.DS2017★ 2 cited

The Garden of Eden theorem: old and new

Tullio Ceccherini-Silberstein, Michel Coornaert

We review topics in the theory of cellular automata and dynamical systems that are related to the Moore-Myhill Garden of Eden theorem.

math.DS2017★ 2 cited

A Garden of Eden theorem for principal algebraic actions

Tullio Ceccherini-Silberstein, Michel Coornaert

Let $Γ$ be a countable abelian group and $f \in Z [Γ]$ , where $Z [Γ]$ denotes the integral group ring of $Γ$ . Consider the Pontryagin dual $X_{f}$ of the cyclic $Z [Γ]$ -module $\Z[Γ]…

math.DS2017★ 4 cited

Surjunctivity and topological rigidity of algebraic dynamical systems

Siddhartha Bhattacharya, Tullio Ceccherini-Silberstein, Michel Coornaert

Let $X$ be a compact metrizable group and $Γ$ a countable group acting on $X$ by continuous group automorphisms. We give sufficient conditions under which the dynamical system $(X,…

math.DS2016

A note on the surjunctivity of algebraic dynamical systems

Tullio Ceccherini-Silberstein, Michel Coornaert

Let $X$ be a compact metrizable group and $Γ$ a countable group acting on $X$ by continuous group automorphisms. We give sufficient conditions under which the dynamical system $(X,…

math.DS2015

Expansive actions of countable amenable groups, homoclinic pairs, and the Myhill property

Tullio Ceccherini-Silberstein, Michel Coornaert

Let $X$ be a compact metrizable space equipped with a continuous action of a countable amenable group $G$ . Suppose that the dynamical system $(X, G)$ is expansive and is the quotien…

math.DS2015

A Garden of Eden theorem for Anosov diffeomorphisms on tori

Tullio Ceccherini-Silberstein, Michel Coornaert

Let $f$ be an Anosov diffeomorphism of the $n$ -dimensional torus $T^{n}$ and $τ$ a continuous self-mapping of $T^{n}$ commuting with $f$ . We prove that $τ$ is sur…

math.GR2014

On Residually Finite Semigroups of Cellullar Automata

Tullio Ceccherini-Silberstein, Michel Coornaert

We prove that if $M$ is a monoid and $A$ a finite set with more than one element, then the residual finiteness of $M$ is equivalent to that of the monoid consisting of all cellular…

math.DS2014

On surjunctive monoids

Tullio Ceccherini-Silberstein, Michel Coornaert

A monoid $M$ is called surjunctive if every injective cellular automata with finite alphabet over $M$ is surjective. We show that all finite monoids, all finitely generated commuta…

math.GR2014

Multipass automata and group word problems

Tullio Ceccherini-Silberstein, Michel Coornaert, Francesca Fiorenzi +2

We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted…

math.DS2013

On sofic monoids

Tullio Ceccherini-Silberstein, Michel Coornaert

We investigate the notion of soficity for monoids. A group is sofic as a group if and only if it is sofic as a monoid. All finite monoids, all commutative monoids, all free monoids…

math.DS2013

The Myhill property for cellular automata on amenable semigroups

Tullio Ceccherini-Silberstein, Michel Coornaert

Let $S$ be a cancellative left-amenable semigroup and let $A$ be a finite set. We prove that every pre-injective cellular automaton $τ : A^{S} \to A^{S}$ is surjective.