abs f ' (fixpoint) = 0

[tommy1729]

it might be standard theory ( in complex dynamical or so ), but im intrested in fixpoints with abs(f ' (fixp)) = 0.

special attention already goes to fixpoints with abs = 1 (parabolic) but abs = 0 seems intresting too.

a classical example is x^2 , it has a 'flat' fixpoint 0 and an ordinary at 1.

( srr for the informal talk here )

[bo198214]

it might be standard theory ( in complex dynamical or so ), but im intrested in fixpoints with abs(f ' (fixp)) = 0.

special attention already goes to fixpoints with abs = 1 (parabolic) but abs = 0 seems intresting too.

a classical example is x^2 , it has a 'flat' fixpoint 0 and an ordinary at 1.

( srr for the informal talk here )

Keyword Boettcher equation.

[tommy1729]

thanks Bo.

one might wonder why i use abs = 0 instead of 0.

that brings me to the following , suppose im not working with the complex numbers , but some 3d or higher dim numbers that have zero-divisors.

if the fixpoint has f ' ( fix ) = zero-divisor , does boettcher equation still work ?