Geodesic
Une propriété de domination convexe pour les orbites sturmiennes
Canadian journal of mathematics, Tome 67 (2015) no. 1, pp. 90-106

Voir la notice de l'article provenant de la source Cambridge University Press

Let $\mathbf{x}\,=\,\left( {{x}_{0}},\,{{x}_{1}},.\,.\,. \right)$ be a $N$ -periodic sequence of integers $\left( N\,\ge \,1 \right)$ , and $\mathbf{s}$ a sturmian sequence with the same barycenter (and also $N$ -periodic, consequently). It is shown that, for affine functions $\alpha :\,\mathbb{R}_{(N)}^{\mathbb{N}}\,\to \,\mathbb{R}$ which are increasing relatively to some order ${{\le }_{2}}$ on $\mathbb{R}_{(N)}^{\mathbb{R}}$ (the space of all $N$ -periodic sequences), the average of $\left| \alpha\right|$ on the orbit of $\mathbf{x}$ is greater than its average on the orbit of $\mathbf{s}$ .
DOI : 10.4153/CJM-2014-009-8
Mots-clés : 37D35, 49N20, 90C27, suite sturmienne, domination convexe, optimisation ergodique 
Bousch, Thierry. Une propriété de domination convexe pour les orbites sturmiennes. Canadian journal of mathematics, Tome 67 (2015) no. 1, pp. 90-106. doi: 10.4153/CJM-2014-009-8
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