Additive perturbed generalized Mandelbrot-Julia sets

作者：Wang Xing yuan^*; Chang Pei jun; Gu Ni ni

来源：Applied Mathematics and Computation, 2007, 189(1): 754-765.

DOI：10.1016/j.amc.2006.11.137

• additive perturbation
• generalized M-J sets
• fractals
• chaos
• Brownian movement

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.

• 出版日期2007-6-1
• 单位大连理工大学