Dynamical Systems Seminar

# Mixing properties of erasing interval maps

## by Prof. Alessandro Della Corte (Università di Camerino)

Europe/Rome
Centro de Giorgi - SNS

#### Centro de Giorgi - SNS

Description

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