Alright, testing the left hand right hand limit I get different values....

I'll refer to from now on.

So therefore:

and

And finally, I'd like to post a question for anyone more familiar with iteration dynamics than me. This is the open problem to extend

if

then:

and so solving for [2, 3] is solving for the iterate of f(1).

f(z) is an analytic function since it's composed of analytic functions and q is restricted to [0,1].

hmmm, so the values come close to each other but don't quite make it. I wonder, does this disqualify it considering it's not analytic at t=1 and the derivative is undefined?

The only case where it is analytic and it is defined is

Which of course I tested using code over the exponential period [1, 2].

i.e.:

But I think that makes it even more beautiful, the fact that it's only analytic at 1 when a, b = e

And finally, I'd like to post a question for anyone more familiar with iteration dynamics than me. This is the open problem to extend

if

then:

and so solving for [2, 3] is solving for the iterate of f(1).

f(z) is an analytic function since it's composed of analytic functions.

I'll refer to from now on.

So therefore:

and

And finally, I'd like to post a question for anyone more familiar with iteration dynamics than me. This is the open problem to extend

if

then:

and so solving for [2, 3] is solving for the iterate of f(1).

f(z) is an analytic function since it's composed of analytic functions and q is restricted to [0,1].

hmmm, so the values come close to each other but don't quite make it. I wonder, does this disqualify it considering it's not analytic at t=1 and the derivative is undefined?

The only case where it is analytic and it is defined is

Which of course I tested using code over the exponential period [1, 2].

i.e.:

But I think that makes it even more beautiful, the fact that it's only analytic at 1 when a, b = e

And finally, I'd like to post a question for anyone more familiar with iteration dynamics than me. This is the open problem to extend

if

then:

and so solving for [2, 3] is solving for the iterate of f(1).

f(z) is an analytic function since it's composed of analytic functions.