08/07/2022, 05:27 PM
Yeah, I also need a pause. Just summarising:
We can have a real analytic function with two fixed points (say left is attracting and right is repelling) such that the analytic continuation of the regular iteration at the first fixed point is the regular iteration at the second fixed point.
In the complex case we can even have vicinities independent of t around each fixed point such that there is a connecting continuation for each t.
However it seems in no case one can have a continuation path independent of t, or: One can not have a domain D containing both fixed points, such that all the iterations of an iteration semi group are analytic on D.
We can have a real analytic function with two fixed points (say left is attracting and right is repelling) such that the analytic continuation of the regular iteration at the first fixed point is the regular iteration at the second fixed point.
In the complex case we can even have vicinities independent of t around each fixed point such that there is a connecting continuation for each t.
However it seems in no case one can have a continuation path independent of t, or: One can not have a domain D containing both fixed points, such that all the iterations of an iteration semi group are analytic on D.
