Dynamical Systems Seminar

Mixing properties of erasing interval maps

by Prof. Alessandro Della Corte (Università di Camerino)

Centro de Giorgi - SNS

Centro de Giorgi - SNS


We study the measurable dynamical properties of the interval map 

generated by the model-case erasing substitution $\rho$, defined by: 
$ \rho(00) = empty word$; ?$\rho(01) = 1$; $\rho?(10) = 0$; $\rho(11) = 01$. 
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. 
KEYWORDS: Mixing; Substitutions; Combinatorics on Words.

Organized by

P. Giulietti