From cubic Newton maps to cubic polynomials – tour of Mandelbrot-like sets
speaker: Krzysztof Baranski (University of Warsaw)abstract: In 1983, Curry, Garnett and Sullivan described Mandelbrot-like sets in the parameter plane of cubic Newton maps. Such sets appear also in some one-dimensional complex slices of the parameter space of cubic polynomials, as shown by Branner and Hubbard in 1992. In this talk we show that one can connect the two kinds of the Mandelbrot-like sets within the (two-complex-dimensional) parameter space of cubic rational maps with two supersinks, which contains both cubic Newton maps and cubic polynomials with a supersink as one-dimensional complex slices. More precisely, starting from a Mandelbrot-like set in cubic Newton maps, one can construct a continuous path of Mandelbrot-like sets ending in the slice composed of cubic maps with two supersinks and a parabolic fixed point of multiplier 1. Then the path bifurcates into two paths of Mandelbrot-like sets, contained respectively in cubic maps with so-called exotic or non-exotic superattracting invariant basins. The non-exotic path ends at a Mandelbrot-like set contained in cubic polynomials with a supersink.
timetable:
Mon 27 May, 11:30 - 12:20, Aula Dini
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