Excuse me Daniel... let \(f:X\to X\) be a function, I'd call an iteration of \(f\) an action of an abelian group \(A\) on \(X\) s.t. for some \(u\in A\) we have \(f_u=f\). In other words, when we talk about iteration I believe that it goes without saying that we assume the law \[f_{a+b}=f_a\circ f_b\] to hold on the nose and not only asymptotically.
So my question is: why don't you ask your solutions to satisfy \(f_{a+b}=f_a\circ f_b\) directly instead of \(f_{a+b}-(f_a\circ f_b) \in \mathcal O({\rm id}^k)\)?
I'm totally newbye in this so I understand like 1% of this thread... maybe Daniel, if you could be a bit more detailed on your assumptions and "story-tell" it a bit it may be easier for non-specialists like me...
So my question is: why don't you ask your solutions to satisfy \(f_{a+b}=f_a\circ f_b\) directly instead of \(f_{a+b}-(f_a\circ f_b) \in \mathcal O({\rm id}^k)\)?
I'm totally newbye in this so I understand like 1% of this thread... maybe Daniel, if you could be a bit more detailed on your assumptions and "story-tell" it a bit it may be easier for non-specialists like me...
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)