(08/28/2022, 01:32 PM)Leo.W Wrote: I'd love to know what the disagreement is against, James
And I wonder where can I browse his works? I want to learn about how much has he did and study more
Oh not quite a disagreement. I think you have just misunderstood me. But when you create a class of functions such that \(f(g) = g(f)\), you do not essentially describe fractional iterates. Because alternative classes of these functions exist. So it is not fundamental, in the sense that you write \(f(g) = g(f)\)--it doesn't entirely determine the space. It restricts values on the space, but doesn't solve it. This is a standard issue theorem in category theory (I know it from abstract algebra, personally). I'm just trying my best to reexplain the initial partial objections Mphlee had. He explained it much better, but you have to read the 100 or so pages Mphlee has posted on this forum. I'm not trying to be a stick in the mud, Leo
I love your work! But we need to always understand the limitations.