In studying dynamical systems, we often use algebraic tools to determine the dynamical behavior of a given function. However, when working with a transcendental function such as the real Weierstrass elliptic function, ℘, we must employ different means. In this thesis we utilize the Schwarzian derivative to find an upper bound on the number of attracting fixed points for the family of functions when the constant g3 > 0. Additionally, we use inherent properties of ℘ to show that the Julia set for this particular class of functions is Cantor when ℘ has an attracting fixed point.