Periodic attractors of random truncator maps

Details Periodic attractors of random truncator maps Periodic attractors of random truncator maps

2006-06-27

arxiv.org/abs/math/0606667v1

Mathematics

Probability

8 pages, presented at APFA5

Scientific paper

10.1016/j.physa.2007.02.090

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.

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