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arXiv · 2206.08000

Cram\'er distance and discretizations of circle expanding maps II: simulations

Pierre-Antoine Guihéneuf·Maurizio Monge
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Abstract

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 arXiv:2206.07991 [math.DS]. Our aim is to identify the phenomena driving the evolution of the Cram\'er distance between the $t$-th iterate of Lebesgue measure by the dynamics $f$ and the $t$-th 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.

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Pierre-Antoine Guihéneuf, Maurizio Monge. 2022-06-16. Cram\'er distance and discretizations of circle expanding maps II: simulations. https://arxiv.org/abs/2206.08000

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