08/21/2022, 01:18 AM
Quick question, I'm a little confused here.
Is this still guessing the asymptotics of a "half root" at a parabolic fixed point?
Or is it something different, (sorry just a tad confused).
If this is happening elsewhere though; maybe Borel summation would be a valuable method of approaching fractional iteration?
By which we could get similar Euler expressions (Like how Euler analytically defines \(\sum_k (-1)^kk! z^k\)) of half iterates (and arbitrary iterates) using some kind of modified Laplace transform. All we would need is a bound like \(j_k = O(c^kk!)\).
Is this still guessing the asymptotics of a "half root" at a parabolic fixed point?
Or is it something different, (sorry just a tad confused).
If this is happening elsewhere though; maybe Borel summation would be a valuable method of approaching fractional iteration?
By which we could get similar Euler expressions (Like how Euler analytically defines \(\sum_k (-1)^kk! z^k\)) of half iterates (and arbitrary iterates) using some kind of modified Laplace transform. All we would need is a bound like \(j_k = O(c^kk!)\).
