11/12/2009, 03:23 PM
actually I think that the regular tetration at the lower fixed point is not continuable to bases
.
Actually I think the Shell-Thron region is the domain of holomorphy, every point on the boundary is singular. This became clear to me some days ago:
1. The regular iteration depends on the derivative of
at the fixed point.
2. If
is the fixed point then the derivation is )
3. The fixed point is given by
, or
.
4. The problematic value of the derivation at the fixed point is
. In this case
is not analytic at
. I guess this implies that
is not analytic at
.
5.
is exactly at those
in the image of the unit circle under of the inverse of
, i.e. under
which is just the boundary of the Shell-Thron region.
Actually I think the Shell-Thron region is the domain of holomorphy, every point on the boundary is singular. This became clear to me some days ago:
1. The regular iteration depends on the derivative of
2. If
3. The fixed point is given by
4. The problematic value of the derivation at the fixed point is
5.