# 2004 - Matt Halstead - 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.

 Download 2004 - Matt Halstead - Dynamics of the Cosine-root Family PDF Document - Size: 3 MB
School of Humanities and Sciences  ·  201 Muller Center  ·  Ithaca College  ·  Ithaca, NY 14850  ·  (607) 274-3102  ·  Full Directory Listing