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On the complete chaotic transformations that preserve symmetric invariant densities

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  • Huang, Weihong

Abstract

A transformation f:[0,1]→[0,1] is said to be complete chaotic if it is (i) ergodic with respect to the Lebesgue measure and (ii) chaotic in the probabilistic sense, that is, an absolutely continuous invariant density φ is preserved. The characteristics of the complete chaotic transformations that preserve symmetric invariant densities, that is, φ(x)=φ(1-x), for all x∈[0,1], are explored. It is found that such transformations are “invariant” with both horizontal and vertical mirroring operations in the sense that the transformations resulted do not only remain to be chaotic but also preserve an identical invariant density. Numerical examples and computer simulations are consistent with theoretical findings.

Suggested Citation

  • Huang, Weihong, 2008. "On the complete chaotic transformations that preserve symmetric invariant densities," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1065-1074.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:4:p:1065-1074
    DOI: 10.1016/j.chaos.2007.01.014
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    References listed on IDEAS

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    1. Huang, Weihong, 2005. "On complete chaotic maps with tent-map-like structures," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 287-299.
    2. Huang, Weihong, 2005. "Characterizing chaotic processes that generate uniform invariant density," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 449-460.
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    2. Huang, Weihong, 2005. "Characterizing chaotic processes that generate uniform invariant density," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 449-460.

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