Abstract
The parameter and dynamic spaces of the cubic mappings consist of many small copies of the Mandelbrot-like sets and Julia sets, respectively of the standard quadratic mapping z - > z * z + c. We find the effective quadratic mappings for the kth iteration of the cubic mappings in the neighborhood of the centers of these small copies. Thus we are able to calculate the positions, sizes and orientations of these small copies. The structure of the cubic mappings is therefore understood.
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