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Periodic attractors of random truncator maps

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  • Theodosopoulos, Ted
  • Boyer, Robert

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.

Suggested Citation

  • Theodosopoulos, Ted & Boyer, Robert, 2007. "Periodic attractors of random truncator maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 302-310.
    • Handle: RePEc:eee:phsmap:v:382:y:2007:i:1:p:302-310
    DOI: 10.1016/j.physa.2007.02.090
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    References listed on IDEAS

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    1. Theodosopoulos, Ted & Yuen, Ming, 2007. "Properties of the wealth process in a market microstructure model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 443-452.
    2. Ted Theodosopoulos, 2004. "Uncertainty relations in models of market microstructure," Papers math/0409076, arXiv.org, revised Feb 2005.
    3. Kaizoji, Taisei & Bornholdt, Stefan & Fujiwara, Yoshi, 2002. "Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 441-452.
    4. Theodosopoulos, Ted, 2005. "Uncertainty relations in models of market microstructure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 209-216.
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