The Perturbed Rat

Re λ	0.001
Im λ

Recently, Blanchard, Devaney, Garijo, and Russell have studied rational maps of the form

F

λ

(z)=

n

z

+λ

-n

z

+c

, where

λ

and

c

are complex-valued parameters. This Demonstration considers the special case when

c=-

and

n=3

. When both the real and imaginary parts of

λ

are equal to zero, we obtain a Julia set called "the rat". When

λ

is nonzero, there is a pole of order three at the origin that changes the structure of the Julia set and perturbs the rat.