05/04/2009, 08:46 PM

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

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