Spectra of stochastic adding machines based on Cantor Systems of numeration

Abstract

In this paper, we define a stochastic adding machine based on Cantor Systems of numeration. We also compute the parts of spectra of the transition operator associated to this stochastic adding machine in different Banach spaces as $c_0, c$ and $l_α,\; 1 \leq α\leq +\infty$. These spectra are connected to fibered Julia sets.