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Noncommutative topological dynamics

Author

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  • Ramos, C. Correia
  • Martins, Nuno
  • Severino, Ricardo
  • Ramos, J. Sousa

Abstract

We study noncommutative dynamical systems associated to unimodal and bimodal maps of the interval. To these maps we associate subshifts and the correspondent AF-algebras and Cuntz–Krieger algebras. As an example we consider systems having equal topological entropy log(1+ϕ), where ϕ is the golden number, but distinct chaotic behavior and we show how a new numerical invariant allows to distinguish that complexity. Finally, we give a statistical interpretation to the topological numerical invariants associated to bimodal maps.

Suggested Citation

  • Ramos, C. Correia & Martins, Nuno & Severino, Ricardo & Ramos, J. Sousa, 2006. "Noncommutative topological dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 15-23.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:1:p:15-23
    DOI: 10.1016/j.chaos.2005.03.016
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    Cited by:

    1. S. Z. Stefanov & Paul P. Wang, 2016. "Day-Ahead Anticipation of Complex Network Vulnerability," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 209-217, November.

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