Eigenvalues of Fibonacci Stochastic Adding Machine

In this work, we compute the eigenvalues of the transition operator associated to the Fibonacci stochastic adding machine. In particular, we show that the eigenvalues are connected to the set [Formula: see text] of complex numbers z where (z 2 , z) belongs to the filled Julia set of a particular endomorphism of ℂ 2 . We also study some topological properties of the set [Formula: see text].