For me it appears roughly like this.
If we have this domain D with the two fixed points contained, then either one fixed point is attracting and attracts some singularity that would then be inside D.
Or points are pushed through between the fixed points (like between the two repelling fixed points in e^x) and then a singularity would also take this path (in this case one might need the *continuous* iteration so that the trajectory cuts the domain D.)
Maybe you were pointing in that direction with your B(z) sets.
If we have this domain D with the two fixed points contained, then either one fixed point is attracting and attracts some singularity that would then be inside D.
Or points are pushed through between the fixed points (like between the two repelling fixed points in e^x) and then a singularity would also take this path (in this case one might need the *continuous* iteration so that the trajectory cuts the domain D.)
Maybe you were pointing in that direction with your B(z) sets.
