STOCHASTIC ADDING MACHINE AND 2-DIMENSIONAL JULIA SETS - Messaoudi, Ali [UNESP]; Uceda, Rafael Asmat (Amer Inst Mathematical Sciences, 2014)
In this work we define a stochastic adding machine associated to a quadratic base (F-n) (n >= 0) formed by recurrent sequences of order 2. We obtain a Markov chain with states in Z(+) and we prove that the spectrum of the transition operator associated to this Markov chain is connected to the filled Julia sets for a class of endomorphisms in C-2 of which we study topological properties.
Keywords: Julia sets; stochastic adding machines; recurrent sequence; Markov chains; spectrum of transition operator