External arguments for the chaotic bands calculation in the Mandelbrot set

Abstract

In this paper we study the chaotic bands of any Mandelbrot set hyperbolic component. We use external arguments in order to identify the hyperbolic components. If we use harmonics as a tool, we can directly calculate the chaotic bands. Indeed, as we clearly show here, the harmonics of the external arguments of a given hyperbolic component (gene) are the external arguments of the last appearance hyperbolic components of the chaotic bands corresponding to the gene. Likewise, we explain some differences in the chaotic region of cardioids and discs.