Periodic attractors of random truncator maps

This paper introduces the \textit{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...

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Bibliographic Details
Published in:arXiv.org 2006-06
Main Authors: Theodosopoulos, Ted, Boyer, Robert
Format: Article
Language:English
Subjects:
Orbits
Online Access:Get full text
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Summary:This paper introduces the \textit{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.
ISSN:2331-8422
DOI:10.48550/arxiv.0606667