### p-Adic Analogues of the Mandelbrot Set

By Jacqueline Anderson

September 11, 2012

#### Abstract

The Mandelbrot set is known for its fractal structure and has inspired
much research in complex dynamics (and many pretty posters for
mathematical events). Its p-adic analogue, however, is boring as can
be - it is simply the unit disk. But, if you generalize this concept
to higher degree polynomials, interesting objects emerge. I will
discuss some background in complex and p-adic dynamics, and explain a
result or two of mine. (I won't assume you know what p-adic numbers
are, but you'll probably get more out of the talk if you do.)