A class of adding machine and Julia sets

2015/08/20 by Danilo Antonio Caprio, Caprio, Danilo Antonio
Computer Science · Mathematics · #Algorithms and Data Compression #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1508.05062

openalex publication_date 2015/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we define a stochastic adding machine associated to the Fibonacci base and to a probabilities sequence p=(p_i)_{i≥ 1}. We obtain a Markov chain whose states are the set of nonnegative integers. We study probabilistic properties of this chain, such as transience and recurrence. We also prove that the spectrum associated to this Markov chain is connected to the fibered Julia sets for a class of endomorphisms in ℂ².

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