SPECTRUM OF STOCHASTIC ADDING MACHINES AND FIBERED JULIA SETS
Nenhuma Miniatura disponível
Data
2013-09-01
Autores
Messaoudi, Ali [UNESP]
Sester, Olivier
Valle, Glauco
Título da Revista
ISSN da Revista
Título de Volume
Editor
World Scientific Publ Co Pte Ltd
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.
Descrição
Palavras-chave
Julia set, Stochastic adding machine, Markov chains, spectrum of transition operator
Como citar
Stochastics And Dynamics. Singapore: World Scientific Publ Co Pte Ltd, v. 13, n. 3, 26 p., 2013.