Rigidity and Toeplitz systems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F25%3AA2603C67" target="_blank" >RIV/61988987:17610/25:A2603C67 - isvavai.cz</a>
Result on the web
<a href="https://www.degruyterbrill.com/document/doi/10.1515/forum-2025-0066/html" target="_blank" >https://www.degruyterbrill.com/document/doi/10.1515/forum-2025-0066/html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/forum-2025-0066" target="_blank" >10.1515/forum-2025-0066</a>

Result language
angličtina
Original language name
Rigidity and Toeplitz systems
Original language description
The aim of this paper is to study measure-theoretical rigidity and partial rigidity for classes of Cantor dynamical systems including Toeplitz systems and enumeration systems. We use Bratteli diagrams to control invariant measures that are produced in our constructions. This leads to systems with desired properties. Among other things, we show that there exists a Toeplitz system with zero entropy that is not partially measure-theoretically rigid with respect to its (unique) invariant measure. We investigate enumeration systems defined by a linear recursion, prove that all such systems are partially rigid and present an example of an enumeration system which is not measure-theoretically rigid. We construct a minimal S-adic Toeplitz subshift which has countably infinitely many ergodic invariant probability measures which are rigid for the same rigidity sequence.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)