Comptes Rendus
no. 11
Functional analysis/Dynamical systems
Generalized adding machines and Julia sets

Presented by: Étienne Ghys

Ali Messaoudi1; Glauco Valle2
1 Universidade Estadual Paulista – Departamento de Matemática do Instituto de Biociências Letras e Ciências Exatas, Rua Cristóvão Colombo, 2265, Jardim Nazareth, 15054-000 São José do Rio Preto, SP, Brazil
2 Universidade Federal do Rio de Janeiro – Departamento de Métodos Estatísticos do Instituto de Matemática, Caixa Postal 68530, 21945-970, Rio de Janeiro, Brazil
Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1096-1100.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.09.009

Ali Messaoudi 1; Glauco Valle 2

1 Universidade Estadual Paulista – Departamento de Matemática do Instituto de Biociências Letras e Ciências Exatas, Rua Cristóvão Colombo, 2265, Jardim Nazareth, 15054-000 São José do Rio Preto, SP, Brazil
2 Universidade Federal do Rio de Janeiro – Departamento de Métodos Estatísticos do Instituto de Matemática, Caixa Postal 68530, 21945-970, Rio de Janeiro, Brazil 
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Ali Messaoudi; Glauco Valle. Generalized adding machines and Julia sets. Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1096-1100. doi : 10.1016/j.crma.2016.09.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.09.009/

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