  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 $l_{\alpha},\; 1 \leq \alpha \leq +\infty$. These spectra are
connected to fibered Julia sets.
