08/22/2007, 07:58 PM
After writing my first paper on defining complex tetration in 1990, I realized that my technique had nothing to do with tetration and could be extended to continuously iterating differentiable functions. Two techniques were published in the mid nineties, one using Bell matrices and the other using another matrix technique, the Carleman linearization technique. So there are three different techniques for continuously iterating functions from the nineties. Their main limitation is that they require a hyperbolic fixed point. The other types of fixed points are exceptional cases. Since two of these techiques are published, the most common type of complex tetration and the complex Ackermann function follow naturally.
Daniel
