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On the Julia set of the perturbed Mandelbrot map. (English) Zbl 0954.37024

Chaos Solitons Fractals 11, No. 13, 2067-2073 (2000); erratum ibid. 12, No. 1, 196 (2001).
The paper deals with the Julia set of the perturbed Mandelbrot map (analytic and non-analytic perturbations). Moreover, the authors also study the Julia set of a Mandelbrot map subject to noise. For low strengths of noise, the Julia set is found to be stable. Increase in the strength of noise results in a deterioration of the shape of the Julia set.

MSC:

37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)
37F50 Small divisors, rotation domains and linearization in holomorphic dynamics
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[1] Kapitaniak T, Andreadis I. On perturbations of the Mandelbrot map. Chaos, Solitons & Fractals 2000;11(7):1131-6; Kapitaniak T, Andreadis I. On perturbations of the Mandelbrot map. Chaos, Solitons & Fractals 2000;11(7):1131-6 · Zbl 0962.37022
[2] Peinke, J.; Parisi, J.; Rĥricht, B.; Rössler, O. E., Instability of the Mandelbrot set, Z Naturforsch, 42A, 263-266 (1986)
[3] Peinke, J.; Parisi, J.; Rĥricht, B.; Rossler, O. E., Smooth decomposition of generalized Fatou set explains smooth structure in generalized Mandelbrot set, Z Naturforsch, 43A, 14-16 (1987) · Zbl 0987.37500
[4] Argyris, J.; Faust, G.; Haase, M., An exploration of chaos (1994), North-Holland: North-Holland Amsterdam
[5] Hermann, D., Algorithmen fur chaos und fracktale (1994), Addison-Wesley: Addison-Wesley Berlin
[6] Peitgen, H. O.; Richter, P. H., The beauty of fractals (1986), Springer: Springer New York · Zbl 0601.58003
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