A stochastic adding machine and complex dynamics

Peter R. Killeen, Thomas Taylor

Research output: Contribution to journalArticle

15 Citations (Scopus)

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 2000

Fingerprint

Complex Dynamics
Markov processes
Julia set
Markov chains
registers
Markov chain
Transition Operator
Quadratic Map
quotients
Failure Time
Natural number
Argand diagram
Increment
integers
Quotient
Binary
operators
Integer
Model

ASJC Scopus subject areas

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

Cite this

A stochastic adding machine and complex dynamics. / Killeen, Peter R.; Taylor, Thomas.

In: Nonlinearity, Vol. 13, No. 6, 11.2000, p. 1889-1903.

Research output: Contribution to journalArticle

Killeen, Peter R. ; Taylor, Thomas. / A stochastic adding machine and complex dynamics. In: Nonlinearity. 2000 ; Vol. 13, No. 6. pp. 1889-1903.
@article{02a5f694320a496ca8f70f8165e65e47,
title = "A stochastic adding machine and complex dynamics",
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.",
author = "Killeen, {Peter R.} and Thomas Taylor",
year = "2000",
month = "11",
doi = "10.1088/0951-7715/13/6/302",
language = "English (US)",
volume = "13",
pages = "1889--1903",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing Ltd.",
number = "6",

}

TY - JOUR

T1 - A stochastic adding machine and complex dynamics

AU - Killeen, Peter R.

AU - Taylor, Thomas

PY - 2000/11

Y1 - 2000/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0034311389&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034311389&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/13/6/302

DO - 10.1088/0951-7715/13/6/302

M3 - Article

VL - 13

SP - 1889

EP - 1903

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 6

ER -