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CHAOS AND FRACTALS IN C–K MAP

XING-YUAN WANG

School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, China

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QING-YONG LIANG

School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, China

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JUAN MENG

School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, China

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https://doi.org/10.1142/S0129183108012935Cited by:10 (Source: Crossref)

Abstract

The characteristic of the fixed points of the Carotid–Kundalini (C–K) map is investigated and the boundary equation of the first bifurcation of the C–K map in the parameter plane is given. Based on the studies of the phase graph, the power spectrum, the correlation dimension and the Lyapunov exponents, the paper reveals the general features of the C–K map transforming from regularity. Meanwhile, using the periodic scanning technology proposed by Welstead and Cromer, a series of Mandelbrot–Julia (M–J) sets of the complex C–K map are constructed. The symmetry of M–J set and the topological inflexibility of distributing of periodic region in the Mandelbrot set are investigated. By founding the whole portray of Julia sets based on Mandelbrot set qualitatively, we find out that Mandelbrot sets contain abundant information of structure of Julia sets.

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