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On complete chaotic maps with tent-map-like structures

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  • Huang, Weihong

Abstract

A unimodal map f : [0,1]→[0,1] is said to be complete chaotic if it is both ergodic and chaotic in a probabilistic sense so as to preserve an absolutely continuous invariant measure. The sufficient conditions are provided to construct complete chaotic maps with the tent-map-like structures, that is, f(x)=1−∣1−2g(x)∣, where g is an one-to-one onto map defined on [0,1]. The simplicity and analytical characteristics of such chaotic maps simplify the calculations of various statistical properties of chaotic dynamics.

Suggested Citation

  • Huang, Weihong, 2005. "On complete chaotic maps with tent-map-like structures," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 287-299.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:1:p:287-299
    DOI: 10.1016/j.chaos.2004.09.021
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    Cited by:

    1. Huang, Weihong, 2008. "On the complete chaotic transformations that preserve symmetric invariant densities," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1065-1074.
    2. Huang, Weihong, 2005. "Characterizing chaotic processes that generate uniform invariant density," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 449-460.
    3. Campos-Cantón, I. & Campos-Cantón, E. & Murguía, J.S. & Rosu, H.C., 2009. "A simple electronic circuit realization of the tent map," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 12-16.

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