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The fermat superfunction
#1
Let f(x) = (x-1)^2 + 1.
If we want the half-iterate of f(x) for x>1 we can use
S(S^[-1](x)+1/2) where S is the superfunction of f(x).

For x>2 this superfunction is F(x) = 2^(2^x) + 1.
Hence I call that the fermat superfunction.

This fermat superfunction F(x) is entire so there are no other branches.

F^[-1] does have branches though but they are easy to understand.

Notice F(x) = 1 has no complex solution.
( 1 is the other fixpoint of f(x) )
But what do we do for the other nonparabolic fixpoint of f(x) ? What superfunction belongs there ?

Is this related to branches of F^[-1] ?

regards

tommy1729
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Messages In This Thread
The fermat superfunction - by tommy1729 - 08/13/2013, 12:23 PM
RE: The fermat superfunction - by tommy1729 - 03/23/2014, 12:15 AM
RE: The fermat superfunction - by mike3 - 03/23/2014, 11:29 PM
RE: The fermat superfunction - by tommy1729 - 03/24/2014, 12:58 AM

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