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Comptes Rendus Mathématique
Volume 354, n° 11
pages 1096-1100 (novembre 2016)
Doi : 10.1016/j.crma.2016.09.009
Received : 2 Mars 2016 ;  accepted : 26 September 2016
Generalized adding machines and Julia sets
Odomètre stochastique et ensembles de Julia
 

Ali Messaoudi a, 1 , Glauco Valle b, 2
a 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 
b Universidade Federal do Rio de Janeiro – Departamento de Métodos Estatísticos do Instituto de Matemática, Caixa Postal 68530, 21945-970, Rio de Janeiro, Brazil 

Abstract

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.

The full text of this article is available in PDF format.
Résumé

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.

The full text of this article is available in PDF format.
1  Supported by CNPq grant 307776/2015-8, Universal CNPq project 482519/2012-6 and FAPESP project 2013/24541-0.
2  Supported by CNPq grant 304593/2012-5 and Universal CNPq project 482519/2012-6.


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