From Newton's method to exotic basins Part II: Bifurcation of the Mandelbrot-like sets
نویسنده
چکیده
This is a continuation of the work Ba] dealing with the family of all cubic rational maps with two supersinks. We prove the existence of a parabolic bifurcation of the Mandelbrot-like sets in the parameter space. Starting from a Mandelbrot-like set in cubic Newton maps and changing parameters in a continuous way, we obtain a parabolic Mandelbrot-like set contained in the family of maps with a xed point of multiplier 1. Then it bifurcates to two paths of Mandelbrot-like sets { one contained in the set of maps with exotic basins and the other in the set of maps with non-exotic basins. The non-exotic path ends at a Mandelbrot-like set in cubic polynomials.
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