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Symbolic dynamics in investigation of quaternionic Julia sets

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  • Lakner, Mitja
  • Škapin-Rugelj, Marjeta
  • Petek, Peter

Abstract

We focus our attention on the dynamics of the simplest quaternionic quadratic function fQ(X)=X2+Q. The discussion can be reduced to a complex parameter Q and a three dimensional subspace. The images of quaternionic Julia sets suggest a natural decomposition. We find that it can be derived from a certain symbolic dynamics giving rise to fractal fibrations. The starting point are the equators and their preimages. If the parameter Q is real, fibrations are trivial, obtained by rotation of the complex Julia set. Repeating itineraries, on the other hand, define curves connecting periodic points.

Suggested Citation

  • Lakner, Mitja & Škapin-Rugelj, Marjeta & Petek, Peter, 2005. "Symbolic dynamics in investigation of quaternionic Julia sets," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1189-1201.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:5:p:1189-1201
    DOI: 10.1016/j.chaos.2004.09.067
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    Cited by:

    1. Lakner, Mitja & Škapin-Rugelj, Marjeta, 2005. "Global invariant manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1533-1540.
    2. Falcão, M. Irene & Miranda, Fernando & Severino, Ricardo & Soares, M. Joana, 2017. "Basins of attraction for a quadratic coquaternionic map," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 716-724.

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