I dont know what you mean, Gottfried, the definition
\( \exp^0(t)=t \)
\( \exp^{n+1}(t)=\exp(\exp^n(t)) \)
uniquely defines \( \exp^n \) for any natural \( n \). This definition is equivalent to if you substitute in the second line
\( \exp^{n+1}(t)=\exp^n(\exp(t)) \).
So the finite iterations are equal and hence also the limit for \( n\to\infty \)!?
But lets continue this discussion of Dmitrii's article in the other thread. As this thread is about cyclic complex functions.
\( \exp^0(t)=t \)
\( \exp^{n+1}(t)=\exp(\exp^n(t)) \)
uniquely defines \( \exp^n \) for any natural \( n \). This definition is equivalent to if you substitute in the second line
\( \exp^{n+1}(t)=\exp^n(\exp(t)) \).
So the finite iterations are equal and hence also the limit for \( n\to\infty \)!?
But lets continue this discussion of Dmitrii's article in the other thread. As this thread is about cyclic complex functions.