Symmetries and Dynamics of Generalized Biquaternionic Julia Sets Defined by Various Polynomials

Symmetries of Julia sets in higher dimensions

Fekete Polynomials and Shapes of Julia Sets

We prove that a nonempty, proper subset S of the complex plane can be approximated in a strong sense by polynomial filled Julia sets if and only if S is bounded and Ĉ \ int(S) is connected. The proof that such a set is approximable by filled Julia sets is constructive and relies on Fekete polynomials. Illustrative examples are presented. We also prove an estimate for the rate of approximation i...

Sierpinski-curve Julia sets and singular perturbations of complex polynomials

In this paper we consider the family of rational maps of the complex plane given by z2 + λ z2 where λ is a complex parameter. We regard this family as a singular perturbation of the simple function z2. We show that, in any neighborhood of the origin in the parameter plane, there are infinitely many open sets of parameters for which the Julia sets of the correspondingmaps are Sierpinski curves. ...

Julia Sets on Rp and Dianalytic Dynamics

We study analytic maps of the sphere that project to well-defined maps on the nonorientable real surface RP. We parametrize all maps with two critical points on the Riemann sphere C∞, and study the moduli space associated to these maps. These maps are also called quasi-real maps and are characterized by being conformally conjugate to a complex conjugate version of themselves. We study dynamics ...

The Julia Sets of Basic Unicremer Polynomials of Arbitrary Degree

Let P be a polynomial of degree d with a Cremer point p and no repelling or parabolic periodic bi-accessible points. We show that there are two types of such Julia sets JP . The red dwarf JP are nowhere connected im kleinen and such that the intersection of all impressions of external angles is a continuum containing p and the orbits of all critical images. The solar JP are such that every angl...