SPECTRUM OF STOCHASTIC ADDING MACHINES AND FIBERED JULIA SETS

Autor(es)

Messaoudi, Ali ^[1] ; Sester, Olivier ^[2] ; Valle, Glauco ^[3]

Afiliação do(s) autor(es)

^[1] UNESP, Dept Matemat, Inst Biociencias Letras & Ciencias, Exatas De Sao Jose Do Ri - Brazil

^[2] Univ Paris Est Marne la Vallee, CNRS, UMR 8050, LAMA, Paris - France

^[3] Univ Fed Rio de Janeiro, Dept Metodos Estat, Inst Matemat, BR-21945970 Rio de Janeiro - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Stochastics and Dynamics; v. 13, n. 3 SEP 2013.
• Citações Web of Science: 4

Resumo

Consider the basic algorithm to perform the transformation n bar right arrow n + 1 changing digits of the d-adic expansion of n one by one. We obtain a family of Markov chains on the non-negative integers through successive and independent applications of the algorithm modified by a parametrized stochastic rule that randomly prevents one of the steps in the algorithm to finish. The objects of study in this paper are the spectra of the transition operators of these Markov chains. The spectra of these Markov chains turn out to be fibered Julia sets of fibered polynomials. This enables us to analyze their topological and analytical properties with respect to the underlying parameters of the Markov chains. (AU)

• Processo FAPESP: 07/06896-5 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Luiz Antonio Barrera San Martin
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 11/23199-1 - Dinâmica de endomorfismos de C2 e conjuntos de Julia
• Beneficiário: André Salles de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil