Spectra of stochastic adding machines based on Cantor Systems of numeration

TL;DR

This paper introduces a stochastic adding machine based on Cantor Systems of numeration and analyzes its spectral properties across various Banach spaces, linking them to fibered Julia sets.

Contribution

It defines a new stochastic adding machine model rooted in Cantor Systems and computes its spectral characteristics in different Banach spaces, connecting to complex dynamics.

Findings

Spectra are computed in spaces c_0, c, and l_α.

Spectral properties are linked to fibered Julia sets.

Provides new insights into the spectral analysis of stochastic systems.

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