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1. CJM 2014 (vol 67 pp. 90)

Bousch, Thierry
Une propriété de domination convexe pour les orbites sturmiennes
Let ${\bf x}=(x_0,x_1,\ldots)$ be a $N$-periodic sequence of integers ($N\ge1$), and ${\bf s}$ a sturmian sequence with the same barycenter (and also $N$-periodic, consequently). It is shown that, for affine functions $\alpha:\mathbb R^\mathbb N_{(N)}\to\mathbb R$ which are increasing relatively to some order $\le_2$ on $\mathbb R^\mathbb N_{(N)}$ (the space of all $N$-periodic sequences), the average of $|\alpha|$ on the orbit of ${\bf x}$ is greater than its average on the orbit of ${\bf s}$.

Keywords:suite sturmienne, domination convexe, optimisation ergodique
Categories:37D35, 49N20, 90C27

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