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arXiv · 1202.4560

Fonction complexité associée à une application ergodique du tore

Jean-François Bertazzon
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Abstract

In this article we give the optimal lower bound for the complexity function of a planar translation which induces an ergodic rotation of the torus $\mathbb{R}^2 / \mathbb{Z}^2$. In addition, we give an explicit calculation of this complexity for the application $(x,y) \mapsto (x+1/ϕ^2,y+x-1/ (2ϕ^3))$, where $ϕ$ is the golden mean. Nous proposons dans ce travail de minorer de manière optimale la fonction complexité associée à une translation du plan, qui induit une rotation ergodique du tore $\mathbb R^2/\mathbb Z^2$. De plus, nous donnons un calcul explicite de cette complexité pour l'application $(x,y)\mapsto(x+1/ϕ^2,y+x-1/(2ϕ^3))$, où $ϕ$ désigne le nombre d'or.

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Jean-François Bertazzon. 2012-02-21. Fonction complexité associée à une application ergodique du tore. https://doi.org/10.1112/blms%2Fbds040

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