### 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 language | English (US) |
---|---|

Pages (from-to) | 1889-1903 |

Number of pages | 15 |

Journal | Nonlinearity |

Volume | 13 |

Issue number | 6 |

DOIs | |

State | Published - Nov 2000 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Nonlinearity*,

*13*(6), 1889-1903. https://doi.org/10.1088/0951-7715/13/6/302

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

Research output: Contribution to journal › Article

*Nonlinearity*, vol. 13, no. 6, pp. 1889-1903. https://doi.org/10.1088/0951-7715/13/6/302

}

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

AN - SCOPUS:0034311389

VL - 13

SP - 1889

EP - 1903

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 6

ER -