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# Une propriété de domination convexe pour les orbites sturmiennes

Published:2014-05-07
Printed: Feb 2015
• Thierry Bousch,
Laboratoire de Mathématique (UMR 8628 du CNRS), bât. 425/430, Université de Paris-Sud, 91405 Orsay Cedex, France
 Format: LaTeX MathJax PDF

## Abstract

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
 MSC Classifications: 37D35 - Thermodynamic formalism, variational principles, equilibrium states 49N20 - Periodic optimization 90C27 - Combinatorial optimization

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