Not to disappoint you either, Leo.W, but *you* missed one thing!
Your explanations might be well and right, however did not address what I was pointing to.
For me Abelian property was just \(f^s\circ f^t=f^t\circ f^s\), because everywhere else Abelian refers to commutativity.
And I just wanted to point out to you that there was more to a continuous iteration - which in turn you pointed out to me! LoL.
Only now when I look back at at one of your answers, I see you meant already \(f^s\circ f^s = f^{s+t}\) by "Abelian property". However I never encountered that naming in some literature. Even when I googled it now, I didn't see clear definitions (On Wikipedia e.g. there is a chapter "Abelian Property" but it is not explicitly defined and they rather use the name "translation functional equation" for non-integers. I always used the name iteration (semi)group - which though is also quite cumbersome to use, because it refers to more than just the equation. So from which literature did you obtain this definition?
Your explanations might be well and right, however did not address what I was pointing to.
For me Abelian property was just \(f^s\circ f^t=f^t\circ f^s\), because everywhere else Abelian refers to commutativity.
And I just wanted to point out to you that there was more to a continuous iteration - which in turn you pointed out to me! LoL.
Only now when I look back at at one of your answers, I see you meant already \(f^s\circ f^s = f^{s+t}\) by "Abelian property". However I never encountered that naming in some literature. Even when I googled it now, I didn't see clear definitions (On Wikipedia e.g. there is a chapter "Abelian Property" but it is not explicitly defined and they rather use the name "translation functional equation" for non-integers. I always used the name iteration (semi)group - which though is also quite cumbersome to use, because it refers to more than just the equation. So from which literature did you obtain this definition?