f( a , x ) C oo tommy1729 Ultimate Fellow     Posts: 1,372 Threads: 336 Joined: Feb 2009 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 tommy1729 Ultimate Fellow     Posts: 1,372 Threads: 336 Joined: Feb 2009 06/17/2009, 04:57 PM (This post was last modified: 06/17/2009, 04:58 PM by tommy1729.) (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... « Next Oldest | Next Newest » 