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On fractal structures in circle geometries. (Über fraktale Strukturen in Kreisgeometrien.) (German) Zbl 0870.58070

The author introduces and studies analogues of the classical fractal sets (Mandelbrot set and Julia sets) in the Minkowski and Laguerre planes. These constructions can be obtained if the standard multiplication of complex numbers is replaced by other operations obtained if \(j^2=1\) (the Minkowski plane) and \(j^2=0\) (the Laguerre plane) instead of \(j^2= -1\).

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
51B15 Laguerre geometries
51B20 Minkowski geometries in nonlinear incidence geometry
28A80 Fractals
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