External arguments of Douady cauliflowers in the Mandelbrot set

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

Research Article Operating with External Arguments of Douady and Hubbard

The external arguments of the external rays theory of Douady and Hubbard is a valuable tool in order to analyze the Mandelbrot set, a typical case of discrete dynamical system used to study nonlinear phenomena. We suggest here a general method for the calculation of the external arguments of external rays landing at the hyperbolic components root points of the Mandelbrot set. Likewise, we prese...

A general view of pseudoharmonics and pseudoantiharmonics to calculate external arguments of Douady and Hubbard

Harmonics give us a compact formula and a powerful tool in order to calculate the external arguments of the last appearance hyperbolic components and Misiurewicz points of the Mandelbrot set in some particular cases. Antiharmonics seem however to have no application. In this paper, we give a general view of pseudoharmonics and pseudoantiharmonics, as a generalization of harmonics and antiharmon...

Operating with external arguments in the Mandelbrot set antenna

The external argument theory of Douady and Hubbard allows us to know both the potential and the field-lines in the exterior of the Mandelbrot set. Nonetheless, there are no explicit formulae to operate with external arguments, and the external argument theory is difficult to apply. In this paper we introduce some tools in order to obtain formulae to operate with external arguments in the Mandel...

Rational External Rays of the Mandelbrot Set

We give a new proof that all external rays of the Mandelbrot set at rational angles land, and of the relation between the external angle of such a ray and the dynamics at the landing point. Our proof is di erent from the original one, given by Douady and Hubbard and re ned by Lavaurs, in several ways: it replaces analytic arguments by combinatorial ones; it does not use complex analytic depende...