Mixing properties of erasing interval maps

We study the measurable dynamical properties of the interval map generated by the model-case erasing substitution $\rho $ , defined by $$ \begin{align*} \rho(00)=\text{empty word},\quad \rho(01)=1,\quad \rho(10)=0,\quad \rho(11)=01. \end{align*} $$ We prove that, although the map is singular, its sq...

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Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 44; no. 2; pp. 408 - 431
Main Authors CORONA, DARIO, DELLA CORTE, ALESSANDRO
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.02.2024
Subjects
Original Article
combinatorics on words
substitutions
mixing
68R15
37A25
28D05
37A05
Online AccessGet full text
ISSN0143-3857
1469-4417
DOI10.1017/etds.2023.16

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Summary:We study the measurable dynamical properties of the interval map generated by the model-case erasing substitution $\rho $ , defined by $$ \begin{align*} \rho(00)=\text{empty word},\quad \rho(01)=1,\quad \rho(10)=0,\quad \rho(11)=01. \end{align*} $$ We prove that, although the map is singular, its square preserves the Lebesgue measure and is strongly mixing, thus ergodic, with respect to it. We discuss the extension of the results to more general erasing maps.
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ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2023.16