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 extra variable ? tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 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 bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 05/04/2009, 09:08 PM (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? « Next Oldest | Next Newest »

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