Interesting phenomenon, I guess it has to do with that the function is not strictly increasing in the vicinity of the second fixed point. If you develop the regular half iterate at the left fixed point it gives a non-real function.

If I remember correctly the matrix power approach even yields a non-real solution if applied at 0 between both fixed point *when the function is strictly increasing*.

For complex fixed points, its anyway (mostly) not the case that the regular iteration at one fixed point has the other fixed point as fixed point.

If I remember correctly the matrix power approach even yields a non-real solution if applied at 0 between both fixed point *when the function is strictly increasing*.

For complex fixed points, its anyway (mostly) not the case that the regular iteration at one fixed point has the other fixed point as fixed point.