Julia Sets of Rational Functions with Special Emphasis on Chebyshev Families, Connentedness, and Visualization on the Computer

Beschreibung

In this thesis we deal with various topics in the field of iterating rational functions in the complex plane, i.e. we investigate certain aspects of Julia and Fatou sets of rational functions. The first major part deals with the iteration of polynomials with only two critical values which leads to the investigation of Chebshev polynomials, multiplied with a constant. These families are investigated in detail, where Mandelbrot-like sets play a crucial role. Another major part of this thesis is devoted to the question whether or not the Julia set of a rational function is connected. We provide various criteria and a new theoretical approach, and we deal with special topics like quasicircles, exotic basins, real functions? The thesis also contains tips, tricks, and implementation details for visualizing Julia sets (and more) on the computer.

Autor*in

Christoph M Stroh

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