Determination of Mandelbrot Sets Hyperbolic Component Centres

In this work we present a very fast and parsimonious method to calculate the centre coordinates of hyperbolic components in the Mandelbrot set. The method we use constitutes an extension for the complex domain of the one developed by Myrberg for the real map x ] x2−p, in which, given the symbolic sequence of a superstable orbit, the parameter value originating such a superstable orbit is worked out. We show that, when dealing with complex domain sequences, some of the solutions obtained correspond to the centres of the Mandelbrot sets hyperbolic components, while some others do not exist.