Cramer distance and discretizations of circle expanding maps II: simulations

This paper presents some numerical experiments in relation with the theoretical study of the ergodic short-term behaviour of discretizations of expanding maps done in P.-A. Guiheneuf and M. Monge, [Cramer distance and discretizations of circle expanding maps I: theory, (2022). arXiv 2206.07991]. Our aim is to identify the phenomena driving the evolution of the distance between the tth iterate of Lebesgue measure by the dynamics f and the tth iterate of the uniform measure on the grid of order N by the discretization on this grid. Based on numerical simulations we propose some conjectures on the effects of numerical truncation from the ergodic viewpoint.