06/23/2009, 05:46 PM

bo198214 Wrote:I played it a little bit. We should take an exponential of the expression I wrote and scale the argument; then it reproduces the kink of reasonable size. Of course, such a probe function does not satisfy the tetration equation, but it shows some reasonabe behavior within the strip along the imaginary axis: after the esponentiation, it has just one kink in the upper halfplane and one in the lower halfplane; this is all we need for the function at the first iteration. We may glue it to the asymptotics, and plot the function even before to make the precise evaluation.Kouznetsov Wrote:Such a function should have some smooth kink of the phase, in order to avoid the jump; but allow such a jump for the principal branch of its logarithm...Can you show me how E(y) would have the behavior as you speculate? Also do the tetrations constructed with other fixed point pairs still satisfy the basic functional equations b[4](z+1) = b^b[4]z and b[4]1=b?

I think about something like