05/27/2011, 10:48 PM
fascinating.
nice answer , but like most nice answers in math , it felt too short.
your answer is very enlightening , but at the same time it brings lots of questions.
holomorphic dynamics is not my thing , but i would love to learn more about it.
however it is hard to ask a formal , clear , direct and good question.
one thing that puzzles me is how the riemann surfaces of the many superfunctions relate to each other ...
also of intrest and similar to the other thread ,
if there are 2m regular superfunctions f_i from one fixpoint , is it true that at least m of those can be chosen such that
f_i(z) = f_j(z + p_q(z) + Q) ??
where p_q(z) is a periodic function and Q is a constant.
another question
if a function F(z) ( not moebius ) has only 2 fixpoints , fixpoint fp1 has N regular superfunctions and fixpoint fp2 has M regular superfunctions , then how many regular superfunctions does F(z) has at most or at minimum ?
its kinda hard to visualize all this ...
nice answer , but like most nice answers in math , it felt too short.
your answer is very enlightening , but at the same time it brings lots of questions.
holomorphic dynamics is not my thing , but i would love to learn more about it.
however it is hard to ask a formal , clear , direct and good question.
one thing that puzzles me is how the riemann surfaces of the many superfunctions relate to each other ...
also of intrest and similar to the other thread ,
if there are 2m regular superfunctions f_i from one fixpoint , is it true that at least m of those can be chosen such that
f_i(z) = f_j(z + p_q(z) + Q) ??
where p_q(z) is a periodic function and Q is a constant.
another question
if a function F(z) ( not moebius ) has only 2 fixpoints , fixpoint fp1 has N regular superfunctions and fixpoint fp2 has M regular superfunctions , then how many regular superfunctions does F(z) has at most or at minimum ?
its kinda hard to visualize all this ...