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Existence Of The Mandelbrot Set In The Parameter Planes Of Certain Rational Functions, Alexander Jay Mitchell
Existence Of The Mandelbrot Set In The Parameter Planes Of Certain Rational Functions, Alexander Jay Mitchell
Theses and Dissertations
In complex dynamics we compose a complex valued function with itself repeatedly and
observe the orbits of values of that function. Particular interest is in the orbit of critical
points of that function (critical orbits). One famous, studied example is the quadratic
polynomial Pc(z) = z^2 +c and how changing the value of c makes a difference to the orbit of the critical point z = 0. The set of c values for which the critical orbit is bounded is called
the Mandelbrot set.
This paper studies rational functions of the form Rn;a;c(z) = z^n + a/z^n + c and …