extra variable ? - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- 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?