Work

On partial rigidity of $\mathcal {S}$ -adic subshifts

Year: 2025

Type: article

Abstract: We develop combinatorial tools to study partial rigidity within the class of minimal $\mathcal {S}$ -adic subshifts. By leveraging the combinatorial data of well-chosen Kakutani–Rokhlin partitions, we establish a necessary and sufficient condition for partial rigidity. Additionally, we provide an explicit expression to compute the partial rigidity rate and an associated partial rigidity sequence. As applications, we compute the partial rigidity rate for a variety of constant length substitution subshifts, such as the Thue–Morse subshift, where we determine a partial rigidity rate of 2/3. We also exhibit non-rigid substitution subshifts with partial rigidity rates arbitrarily close to 1 and, as a consequence, using products of the aforementioned substitutions, we obtain that any number in $[0, 1]$ is the partial rigidity rate of a system.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2025.4

Authors: SEBASTIÁN DONOSO, ALEJANDRO MAASS, TRISTÁN RADIĆ

Institutions: Centre National de la Recherche Scientifique, Center for Mathematical Modeling, University of Chile, Millennium Institute, Northwestern University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Institut Català de Nanociència i Nanotecnologia, University of Cambridge, Agencia Nacional de Investigación y Desarrollo