arXiv subjects

Michael Schraudner

Publications and source records attributed to Michael Schraudner.

3 recordsLinked to original sources

arXiv2021

A strongly aperiodic shift of finite type on the discrete Heisenberg group using Robinson tilings

We explicitly construct a strongly aperiodic subshift of finite type for the discrete Heisenberg group. Our example builds on the classical aperiodic tilings of the plane due to Raphael Robinson. Extending those tilings to the Heisenberg group by exploiting the group's structure and posing additional local rules to prune out remaining periodic behavior we maintain a rich projective subdynamics on $\mathbb Z^2$ cosets. In addition the obtained subshift factors onto a strongly aperiodic, minimal sofic shift via a map that is invertible on a dense set of configurations.

math.DS↗

arXiv2020

Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag-Solitar groups $BS(1,n)$

We present a technique to lift some tilings of the discrete hyperbolic plane -- tilings defined by a 1D substitution -- into a zero entropy subshift of finite type (SFT) on non-abelian amenable Baumslag-Solitar groups $BS(1,n)$ for $n\geq2$. For well chosen hyperbolic tilings, this SFT is also aperiodic and minimal. As an application we construct a strongly aperiodic SFT on $BS(1,n)$ with a hierarchical structure, which is an analogue of Robinson's construction on $\mathbb{Z}^2$ or Goodman-Strauss's on $\mathbb{H}_2$.

math.DS↗

arXiv2013

Speed of convergence for the realization of an effective subshift by a multidimensional SFT or Sofic

Realization of $d$-dimensional effective subshifts as projective sub-actions of $d+d'$-dimensional sofic subshifts for $d'\geq 1$ is now well know~\cite{Hochman-2009,Durand-Romashchenko-Shen-2010,Aubrun-Sablik-2010}. In this paper we are interested in the speed of convergence of this realization. That is to say given an effective subshift $Σ$ realized as projective sub-action of a sofic $\T$, we study the function which on input an integer $k$ returns the smallest width of the strip which verify the local rules of $\T$ necessary to obtain exclusively the language of size $k$ of $Σ$ in the central row of the strip. We study this topological conjugacy invariant for effective subshifts in order to exhibit algorithmic properties of these subshifts.

math.DS↗