Determination of Mandelbrot Sets Hyperbolic Component Centres

✍ Scribed by G. Álvarez; M. Romera; G. Pastor; F. Montoya

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 642 KB
• Volume: 9
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(98)00046-0

✦ Synopsis

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 Ł x 1 -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 set|s hyperbolic components\ while some others do not exist[ Þ 0887 Elsevier Science Ltd[ All rights reserved[ Author for correspondence [ E!mail] gonzaloÝiec[csic[es[