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+--- Thread: f( a , x ) C oo (/showthread.php?tid=303)
f( a , x ) C oo - tommy1729 - 06/12/2009
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
RE: f( a , x ) C oo - tommy1729 - 06/17/2009
(06/12/2009, 12:27 PM)tommy1729 Wrote: 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
the answers are yes.
(06/17/2009, 04:57 PM)tommy1729 Wrote:(06/12/2009, 12:27 PM)tommy1729 Wrote: 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
the answers are yes.
matrix thinking was key...