Dynamics of the Cosine-root Family

ABSTRACT
We will investigate the chaotic dynamics of the complex cosine-root family, $\C(z)=\alpha\cos{\sqrt{z+\beta}}$, where $\alpha,\beta,z\in\mathbb{C}$. We show how to approximate the Julia set of each $\C$ and discuss some of its features. We also plot parameter space pictures, highlighting phenomena resembling that of quadratic polynomials. Finally, we make an analysis of super-attracting cycles for this family.

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