# The Perturbed Rat

The Perturbed Rat

Recently, Blanchard, Devaney, Garijo, and Russell have studied rational maps of the form , where and are complex-valued parameters. This Demonstration considers the special case when and . When both the real and imaginary parts of are equal to zero, we obtain a Julia set called "the rat". When is nonzero, there is a pole of order three at the origin that changes the structure of the Julia set and perturbs the rat.

F(z)=z+λz+c

λ

n

-n

λ

c

c=-

n=3

λ

λ