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Pré-Publication, Document De Travail Année : 2022

Discrepancy and discretizations of circle expanding maps II: simulations

Résumé

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 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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Dates et versions

hal-03883535 , version 1 (03-12-2022)
hal-03883535 , version 2 (01-11-2023)

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Pierre-Antoine Guihéneuf, Maurizio Monge. Discrepancy and discretizations of circle expanding maps II: simulations. 2022. ⟨hal-03883535v1⟩
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