[Odomètre stochastique et ensembles de Julia]
Nous définissons l'odomètre stochastique associé à un système de numération de Cantor. Nous calculons les parties du spectre de l'opérateur de transition associé à cet odométre dans différents espaces de Banach classiques. Nous montrons que le spectre est lié aux ensembles de Julia fibrés.
We define stochastic adding machines based on Cantor Systems of numeration. Our aim here is to compute the parts of spectra of the transition operators associated with these stochastic adding machines in different classical Banach spaces. We show that these spectra are connected to fibered Julia sets.
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@article{CRMATH_2016__354_11_1096_0,
author = {Messaoudi, Ali and Valle, Glauco},
title = {Generalized adding machines and {Julia} sets},
journal = {Comptes Rendus. Math\'ematique},
pages = {1096--1100},
publisher = {Elsevier},
volume = {354},
number = {11},
year = {2016},
doi = {10.1016/j.crma.2016.09.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.09.009/}
}
TY - JOUR AU - Messaoudi, Ali AU - Valle, Glauco TI - Generalized adding machines and Julia sets JO - Comptes Rendus. Mathématique PY - 2016 SP - 1096 EP - 1100 VL - 354 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.09.009/ DO - 10.1016/j.crma.2016.09.009 LA - en ID - CRMATH_2016__354_11_1096_0 ER -
%0 Journal Article %A Messaoudi, Ali %A Valle, Glauco %T Generalized adding machines and Julia sets %J Comptes Rendus. Mathématique %D 2016 %P 1096-1100 %V 354 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.09.009/ %R 10.1016/j.crma.2016.09.009 %G en %F CRMATH_2016__354_11_1096_0
Messaoudi, Ali; Valle, Glauco. Generalized adding machines and Julia sets. Comptes Rendus. Mathématique, Tome 354 (2016) no. 11, pp. 1096-1100. doi : 10.1016/j.crma.2016.09.009. http://www.numdam.org/articles/10.1016/j.crma.2016.09.009/
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