A stochastic adding machine and complex dynamics

Peter R. Killeen, Thomas Taylor

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

This paper considers properties of a Markov chain on the natural numbers which models a binary adding machine in which there is a non-zero probability of failure each time a register attempts to increment the succeeding register and resets. This chain has a family of natural quotient Markov chains, and extends naturally to a chain on the 2-adic integers. The transition operators of these chains have a self-similar structure, and have a spectrum which is, variously, the Julia set or filled Julia set of a quadratic map of the complex plane.

Original languageEnglish (US)
Pages (from-to)1889-1903
Number of pages15
JournalNonlinearity
Volume13
Issue number6
DOIs
StatePublished - Nov 1 2000

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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