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Computing the topological entropy of continuous maps with at most three different kneading sequences with applications to Parrondo’s paradox

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  • Cánovas, Jose S.
  • Guillermo, María Muñoz

Abstract

We introduce an algorithm to compute the topological entropy of piecewise monotone maps with at most three different kneading sequences, with prescribed accuracy. As an application, we compute the topological entropy of 3-periodic sequences of logistic maps, disproving a commutativity formula for topological entropy with three maps, and analyzing the dynamics Parrondo’s paradox in this setting.

Suggested Citation

  • Cánovas, Jose S. & Guillermo, María Muñoz, 2016. "Computing the topological entropy of continuous maps with at most three different kneading sequences with applications to Parrondo’s paradox," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 1-17.
    • Handle: RePEc:eee:chsofr:v:83:y:2016:i:c:p:1-17
    DOI: 10.1016/j.chaos.2015.10.036
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    References listed on IDEAS

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    1. Matsumoto, Akio & Nonaka, Yasuo, 2006. "Statistical dynamics in a chaotic Cournot model with complementary goods," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 769-783, December.
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    Cited by:

    1. Jia, Shuyi & Lai, Joel Weijia & Koh, Jin Ming & Xie, Neng Gang & Cheong, Kang Hao, 2020. "Parrondo effect: Exploring the nature-inspired framework on periodic functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).

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