Chaotic bands in the Mandelbrot set

External arguments for the chaotic bands calculation in the Mandelbrot set

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 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 hyperboli...

Equivalence between Subshrubs and Chaotic Bands in the Mandelbrot Set

We study in depth the equivalence between subshrubs and chaotic bands in the Mandelbrot set. In order to do so, we introduce the rules for chaotic bands and the rules for subshrubs, as well as the transformation rules that allow us to interchange them. From all the denominations of a chaotic band, we show the canonical form; that is, the one associated to the hyperbolic component that generates...

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

Application of Gray code to the cryptanalysis of chaotic cryptosystems

Gray codes have found many applications in engineering and mathematics. In this work we explain how to apply Gray codes to the determination of the control parameter and initial point of a chaotic orbit generated by the Mandelbrot map when the kneading sequence is known. Possible applications to the cryptanalysis of a certain type of cryptosystems based on Baptista’s algorithm are also discussed.

New approach to ε - entropy and Its compa rison with Kolmogorov ’ s ε - entropy

Kolmogorov introduced a concept of ε-entropy to analyze information in classical continuous system. The fractal dimension of geometrical sets was introduced by Mandelbrot as a new criterion to analyze the complexity of these sets. The ε-entropy and the fractal dimension of a state in general quantum system were introduced by one of the present authors in order to characterize chaotic properties...