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abs f ' (fixpoint) = 0
#1
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 )
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#2
(09/08/2010, 07:59 PM)tommy1729 Wrote: 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.

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#3
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 ?
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