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Stochastic adding machine and $2$-dimensional Julia sets

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  • In this work we define a stochastic adding machine associated to a quadratic base $(F_n)_{n \geq 0}$ formed by recurrent sequences of order 2. We obtain a Markov chain with states in $\mathbb{Z}^+$ 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 $\mathbb{C}^2$ of which we study topological properties.
    Mathematics Subject Classification: Primary: 37A30, 37F50; Secondary: 47A10.

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