[2014] composition of 3 functions. - 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: [2014] composition of 3 functions. (/showthread.php?tid=915) [2014] composition of 3 functions. - tommy1729 - 08/25/2014 I want to consider composition of 3 nonlinear analytic functions. Lets require that composition is noncommutative. Denote composition with & and the functions with A,B,C. A & B & C = B & C & A = C & A & B = T1 A & C & B = C & B & A = B & A & C = T2 T1 =/= T2. This reminds me of quaternions and related stuff. However we are considering functions here instead of numbers. It seems like a natural continuation of algebra and dynamics. Well this or a weaker set of equations. An intresting weaker set of equations is A & B & C = B & C & A = C & A & B = T1 {A & C & B , C & B & A , B & A & C }= T2 T1 is not equal to any member of the set T2. I was inspired by being bored with f^[a+b] = f^[a](f^[b]) = f^[b](f^[a]) or chebyshev type polynomials. The commutative property started to feel like a prison for my mind. We want more functions and concepts than just commutative. regards tommy1729