On Stochastic Adding Machines and Non-Autonomous Julia Sets

Abstract

This work investigates the spectral and dynamical properties of transition operators associated with a class of stochastic adding machines. In particular, we characterize the spectra of these operators in terms of non-autonomous Julia sets. This description, in turn, provides new information about their dynamical behavior, including criteria for supercyclicity and hypercyclicity.

22 pages, 7 figures