In this paper we consider the dynamical behavior of the family of complex rational maps given by where n ≥ 2, d ≥ 1. Despite the high degree of these maps, there is only one free critical orbit up to… Expand

This work gives sufficient conditions on a lattice for which the corresponding Weierstrass elliptic ℘ function is locally connected and quadratic-like, and uses these results to prove the existence of locally Sierpinski Julia sets for certain elliptic functions.Expand

In this paper we consider the family of rational maps of the complex plane given by \[z^2+\frac{\lambda}{z^2}\] where $\lambda$ is a complex parameter. We regard this family as a singular… Expand

A dynamical invariant determines which of these maps are conjugate on their Julia sets, and it is obtained an exact count of the number of distinct conjugacy classes of maps drawn from these main cardioids.Expand

Stylometric methods are used to provide evidence for a claim about the authorship of the story and to analyze the nature of Eddy’s collaboration with Lovecraft.Expand

In this paper we prove the existence of a new type of Sierpinski
curve Julia set for certain families of rational maps of the
complex plane. In these families, the complementary domains
consist of… Expand

The dynamics of the map is investigated for . This map is derived from multiple geometric circle inversions. Conditions are given for Cantor set and Sierpinski curve Julia sets for this family.

We study the dynamics of a map generated via geometric circle inversion. In particular, we define multiple circle inversion and investigate the dynamics of such maps and their corresponding Julia… Expand