Noncommutative topological dynamics

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

Chaos, Solitons & Fractals, 2006, vol. 27, issue 1, 15-23

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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:27:y:2006:i:1:p:15-23

DOI: 10.1016/j.chaos.2005.03.016

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