Periodic attractors of random truncator maps

Ted Theodosopoulos and Robert Boyer

Physica A: Statistical Mechanics and its Applications, 2007, vol. 382, issue 1, 302-310

Abstract: This paper introduces the truncator map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify its periodic orbits using properties of endomorphisms of the resulting algebraic structure. A stochastic model is constructed on these endomorphisms, which leads to the classification of the distribution of periodic orbits for random truncator maps. This framework is applied to investigate the periodic transitions of Bornholdt's spin market model.

Keywords: Noncommutative algebraic dynamics; Iterated function systems; Periodic orbits; Stochastic endomorphisms (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:382:y:2007:i:1:p:302-310

DOI: 10.1016/j.physa.2007.02.090

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