the inconsistency depending on fixpoint-selection

[Gottfried]

However your second transformation
, ,
has as translation the same translation as in your previous transformation!
Only changes to .

So this second transformation moves also the *greater* fixed point to 0. And we have seen that we can dismiss any multiplicative conjugation with respect to regular iteration. So it has of course the same result (fractional iteration of ) as your first transformation.

Yepp - I just found the position of the error, grmmpff. It is in

Code:

´
using e1=1/4                                e2 = -1/4  
      d1=1/4 / e1 =1                        d2 = 1/4 / e2 = -1

x' =  4x - 1                               x´ = -4x + 1
x" =  (x+1)/4                              x´´= (x-1)/-4

Although I had already that not e or d, but e*d = fixpoint, in the computation of d2, I used the same (1/4) as for d1. For clarity, I should have written a symbol for the selected fixpoint:

Code:

´
involving fixpoint p=1/4                    fixpoint q=-1/4
using e1=1/4                                e2 = -1/4  
      d1=p / e1 =1                          d2 = q / e2 = 1

x' =  4x - 1                               x´ = -4x - 1
x" =  (x+1)/4                              x´´= (x+1)/-4

Hope this corrects things, didn't check it again yet, but it seems that this reflects just the simple sign-changing in the matrices.
The previous G2-matrix and the subsequent considerations in that posting are on a false assumption...

Gottfried