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• W2044773904 abstract "Adopting the experimental mathematics method combining complex variable function theory with computer aided drawing, this paper researches on the structural characteristic and the fission-evolution law of additive perturbed generalized Mandelbrot–Julia sets (generalized M–J sets in short). The corresponding relationship between point coordinates in generalized M set and the general structure of generalized J sets has been founded qualitatively and the physical meaning of the generalized M–J sets has been expounded. The following conclusions are deduced: (1) Chaotic patterns of fractal structure of generalized J sets may emerge out of double-periodic bifurcation, which shows that Brownian movement can be chaotic. (2) Experimental evidence of Li–Yorke theorem is given out. (3) The additive perturbed generalized M set contains abundant information on the construction of generalized J sets. (4) Resemble logistic map, in the process of a series of double-periodic bifurcation coming into chaos, generalized J sets also present self-similarity in parameter space." @default.
• W2044773904 created "2016-06-24" @default.
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• W2044773904 date "2007-06-01" @default.
• W2044773904 modified "2023-10-16" @default.
• W2044773904 title "Additive perturbed generalized Mandelbrot–Julia sets" @default.
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• W2044773904 doi "https://doi.org/10.1016/j.amc.2006.11.137" @default.
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