Combinatorial and dynamical properties of adding machine

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Date(s) - 25/03/2015
0 h 00 min


Soutenance de thèse

In this work we define a stochastic adding machine associated to the Fibonacci base and to a probabilities sequence (Pi) i>1. We obtain a Markov chain whose states are the set of nonnegative integers. We study probabilistic properties of this chain, such as transience and recurrence. We also prove that the spectrum associated to this Markov chain is connected to the filled Julia sets for a class of endomorphisms in C 2. Furthermore, we study topological and dynamical properties of a class of endomorphisms of C 2 (or R 2). Precisely, the considered maps are fn(x, y) = (x y + cn, x), where cn 2 C (or cn E R), for all n>0.

Keywords: Adding machine, Markov chains, transition operator, spectrum, Julia sets, fibered Julia sets

*Membres du jury :

– Prof. Dr. Ali Messaoudi, UNESP – São José do Rio Preto, Orientador
– Prof. Dr. Eduardo Garibaldi, UNICAMP – Campinas
– Prof. Dr. Sylvain Philippe Pierre Bonnot, USP – São Paulo
– Prof. Dr. Paulo Ricardo da Silva, UNESP – São José do Rio Preto
– Prof. Dr. Márcio Ricardo Alves Gouveia, UNESP – São José do Rio Preto

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