Une propriété de domination convexe pour les orbites sturmiennes
Canadian journal of mathematics, Tome 67 (2015) no. 1, pp. 90-106
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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 $\mathbf{s}$ .
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
@article{10_4153_CJM_2014_009_8,
author = {Bousch, Thierry},
title = {Une propri\'et\'e de domination convexe pour les orbites sturmiennes},
journal = {Canadian journal of mathematics},
pages = {90--106},
year = {2015},
volume = {67},
number = {1},
doi = {10.4153/CJM-2014-009-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2014-009-8/}
}
TY - JOUR AU - Bousch, Thierry TI - Une propriété de domination convexe pour les orbites sturmiennes JO - Canadian journal of mathematics PY - 2015 SP - 90 EP - 106 VL - 67 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2014-009-8/ DO - 10.4153/CJM-2014-009-8 ID - 10_4153_CJM_2014_009_8 ER -
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