Work

Cramér distance and discretizations of circle expanding maps II: simulations

Year: 2023

Type: article

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 P.-A. Guihéneuf and M. Monge, [Cramér 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.

Source: Dynamical Systems

DOI: 10.1080/14689367.2023.2236036

Authors: Pierre-Antoine Guihéneuf, Maurizio Monge

Institutions: Centre National de la Recherche Scientifique, Université Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université, Universidade Federal do Rio de Janeiro

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Centre National de la Recherche Scientifique

Award: Computer orbits for Discrete Dynamical Systems