07/13/2011, 03:17 AM
Hi.
Consider the limit of tetration \( ^z b \) as \( b \rightarrow \eta \) from the right, along the real axis (Here, we use the Kneser/etc. tetrational). The tetrational looks to converge to the parabolic attracting regular iteration at base \( \eta \). This suggests that the resulting fractional iterates of \( \exp_b(x) \) converge to the attracting parabolic regular iterates of base \( \eta \) when \( x < e \). But what about \( x > e \)? Does it converge to the iterates obtained from the "cheta" function \( \check{\eta}(x) \)?
Consider the limit of tetration \( ^z b \) as \( b \rightarrow \eta \) from the right, along the real axis (Here, we use the Kneser/etc. tetrational). The tetrational looks to converge to the parabolic attracting regular iteration at base \( \eta \). This suggests that the resulting fractional iterates of \( \exp_b(x) \) converge to the attracting parabolic regular iterates of base \( \eta \) when \( x < e \). But what about \( x > e \)? Does it converge to the iterates obtained from the "cheta" function \( \check{\eta}(x) \)?
