Symbolic dynamics in investigation of quaternionic Julia sets

Mitja Lakner, Marjeta Škapin-Rugelj and Peter Petek

Chaos, Solitons & Fractals, 2005, vol. 24, issue 5, 1189-1201

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.

Date: 2005
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:24:y:2005:i:5:p:1189-1201

DOI: 10.1016/j.chaos.2004.09.067

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