A stochastic adding machine and complex dynamics

Authors: Killeen P.R.¹; Taylor T.J.²

Source: Nonlinearity, Volume 13, Number 6, 2000 , pp. 1889-1903(15)

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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.

Language: English

Document Type: Miscellaneous

Affiliations: 1: Department of Psychology, Arizona State University, Tempe, AZ 85287, USA 2: Department of Mathematics, and Systems Science and Engineering Research Center, Arizona State University, Tempe, AZ 85287, USA

Publication date: 2000-01-01