04/29/2021, 03:02 AM
Hey, Gottfried could you explain more what you mean? Or, what you're intending to compute mathematically? This seems interesting, and I'm rather curious.
I get that you're using \( n \) cycles,
\(
\{z_i\}_{i=0}^{n-1}\,\,\text{s.t}\,\,\exp(z_i) = z_{i+1}\,\,\text{where}\,\,z_n = z_0\\
\)
I get that you're describing this using the inverse Schroder function,
\(
z_i = \Psi(L^i \xi)\,\,\text{for}\,\,\xi \in \mathbb{C}\\
\)
And I assume you're trying to construct Kneser's solution; which is usually done about a fixed point, but somehow you mean to do it about a cycle? I'm genuinely curious as to how one would do that. Are we essentially just performing Kneser's method on,
\(
\exp^{\circ n}(z)\,\,\text{about}\,\,z = z_i\\
\)
Whereupon, we know this solution will still be Kneser (as far as I understand Kneser this will happen; correct me if I'm wrong, but can't one show this by uniqueness?).
I'm just curious if you could link me to threads, or explain what you mean to do here. I apologize if I'm being obtuse. I'm a horrible computer programmer. As much as I've lurked Sheldon's threads about fatou.gp; I wish it was just written in math, lol.
Do you mind if you explained the mathematics of what you're trying to do?
Sincerely, James
I get that you're using \( n \) cycles,
\(
\{z_i\}_{i=0}^{n-1}\,\,\text{s.t}\,\,\exp(z_i) = z_{i+1}\,\,\text{where}\,\,z_n = z_0\\
\)
I get that you're describing this using the inverse Schroder function,
\(
z_i = \Psi(L^i \xi)\,\,\text{for}\,\,\xi \in \mathbb{C}\\
\)
And I assume you're trying to construct Kneser's solution; which is usually done about a fixed point, but somehow you mean to do it about a cycle? I'm genuinely curious as to how one would do that. Are we essentially just performing Kneser's method on,
\(
\exp^{\circ n}(z)\,\,\text{about}\,\,z = z_i\\
\)
Whereupon, we know this solution will still be Kneser (as far as I understand Kneser this will happen; correct me if I'm wrong, but can't one show this by uniqueness?).
I'm just curious if you could link me to threads, or explain what you mean to do here. I apologize if I'm being obtuse. I'm a horrible computer programmer. As much as I've lurked Sheldon's threads about fatou.gp; I wish it was just written in math, lol.
Do you mind if you explained the mathematics of what you're trying to do?
Sincerely, James
