Iteration with two analytic fixed points

[bo198214]

Is this analytic in the domain \(|\Im t| < \delta\) (you can add \(\Re t > 0\), if you like) and \(|x| < \epsilon\)? Both domains fixed?

The claim was that \(x\mapsto f^{\circ t}(x)\) is analytic for all t at 0. I didn't say anything about fixing the domain of analyticity. (Like I said several times this is so restrictive that you can not work with it in most cases. I think you can not even apply it to our beloved base sqrt 2.)

Does that answer your concerns or did you rather claim that it is not analytic even if we don't fix the domain?
Then I would have to investigate further ...