05/04/2008, 07:14 AM
I admit I didnt dive completely into your derivations.
First question what is the parabolic flow matrix?
Is it the Carleman/Bell-Matrix of parabolic iteration \( f^{\circ t}(x) \)?
Why is it then important to know the diagonals? Because the first entry is the coefficient of the series of \( f^{\circ t}(x) \)?
I dont get this, lets look at the double binomial formula, which should give the same coefficients if I understood that right. There are no denominators depending on the value of any \( f_k \). I only know that in hyperbolic iteration there occurs \( f_1^n-f_1 \) in the denominator.
So lets clarify the basics first
First question what is the parabolic flow matrix?
Is it the Carleman/Bell-Matrix of parabolic iteration \( f^{\circ t}(x) \)?
Why is it then important to know the diagonals? Because the first entry is the coefficient of the series of \( f^{\circ t}(x) \)?
andydude Wrote:From these generating functions is it easy to see that parabolic iteration does not work for \( f_2 = 0 \),
which I believe has already been proven by someone, somewhere. What is interesting is that there are actually 2 reasons for this. The first reason is that there are many \( f_2 \) in the denominator, which cannot be zero, and the second reason is that if \( f_2 = 0 \), then \( z=1 \) which means t plays no part in the equations at all.
I dont get this, lets look at the double binomial formula, which should give the same coefficients if I understood that right. There are no denominators depending on the value of any \( f_k \). I only know that in hyperbolic iteration there occurs \( f_1^n-f_1 \) in the denominator.
So lets clarify the basics first