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Rational operators (a {t} b); a,b > e solved
#12
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.
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RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/06/2011, 07:47 PM

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