Abstract
AbstractWe 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.