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+--- Thread: extra variable ? (/showthread.php?tid=288)
extra variable ? - tommy1729 - 05/04/2009
when considering half-iterations we usually consider solutions Coo from
R -> R
or
C -> C
but there are many case where such a solution does not exist , not even in a real interval or a taylor series with positive radius.
even if we weaking our requirements from Coo to analytic or even any function at all , there are still cases without a solution
e.g.
there are no solutions C -> C for a half iterate of 5 x^2 + 4 x + 1 ...
so thus the idea and title of this thread " extra variable ? "
so , for instance , we look for solutions in other spaces apart from R or C.
thus , extra variables/dimensions.
lets say T -> T
( yes , i use T because im 'T'ommy :p )
there are 2 roads
we can look for appropriate extra variables to solve a half-iterate problem.
or we can look for appropriate half-iterate problems for extra variables.
however , its a bit of a gamble whether "extra variables" can be usefull at all ....
its not immediatly clear , if no solution C -> C exists , then does a solution exist for " extra variables " ?
im thinking about R x C and C x C ...
im curious about the existance of previous considerations ...
circulant matrices seems a good start i think ...
let me know what you think ...
regards
tommy1729
RE: extra variable ? - bo198214 - 05/04/2009
(05/04/2009, 08:46 PM)tommy1729 Wrote: there are no solutions C -> C for a half iterate of 5 x^2 + 4 x + 1 ...
why not?