06/12/2009, 12:27 PM
many ideas of mine about tetration are related to talking the limit
lim a -> 0 g(g(x)) = f ( a , x )
where g has a single real fixed point for all a > 0 but not for a = 0 and the half iterate is thus computed " regularly ".
now the 2 big questions are :
in such cases as above ( such as 1 real fixed point for a > 0 )
g(x) depends on "a".
lets say : g(x,a).
IS g(x,a) Coo with respect to a ?
IS the radius of convergeance with respect to x Coo with respect to a ?
regards
tommy1729
lim a -> 0 g(g(x)) = f ( a , x )
where g has a single real fixed point for all a > 0 but not for a = 0 and the half iterate is thus computed " regularly ".
now the 2 big questions are :
in such cases as above ( such as 1 real fixed point for a > 0 )
g(x) depends on "a".
lets say : g(x,a).
IS g(x,a) Coo with respect to a ?
IS the radius of convergeance with respect to x Coo with respect to a ?
regards
tommy1729