The Mandelbrot Set and Julia Sets
Change of Variables
Take z = v/(a
n
)
1/n
. Then
a
n
z
n
+ a
n-1
z
n-1
+ ... + a
1
z + a
0
= a
n
(v/(a
n
)
1/n
)
n
+ a
n-1
(v/(a
n
)
1/n
)
n-1
+ ... a
1
(v/(a
n
)
1/n
) + a
0
= v
n
+ (a
n-1
/a
n
(n-1)/n
)v
n-1
+ ... + (a
1
/a
n
1/n
)v + a
0
Polynomials with first coefficient 1 are called
monic
. This change of variables shows we may assume the polynomial function is monic.
Return to
Change of Variables
.