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Romera, M.; Pastor, G.; Álvarez, G.; Montoya, F.

Shrubs in the Mandelbrot set ordering. (English) Zbl 1057.37048

Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 8, 2279-2300 (2003).
Summary: We introduce shrubs in this paper in order to present a first approach to studying the structure of the Mandelbrot set. Primary, secondary\(\dots\)and \(N\)-ary shrubs are analyzed. We have experimentally obtained formulae to calculate the periods of the hyperbolic component representatives of the structural branches, and the preperiods and periods of both the nodes – where structural branches emanate – and the tips – where the shrub enters in crisis. A generalization allows us to give in each case one formula to calculate representative periods and preperiods and periods of nodes and tips.

Cited in 5 Documents

MSC:

37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)

Keywords:

Mandelbrot set; hyperbolic components; Misiurewicz points
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\textit{M. Romera} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 8, 2279--2300 (2003; Zbl 1057.37048)
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