The mystery of 2 fixpoints. - 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: The mystery of 2 fixpoints. ( /showthread.php?tid=856) |

The mystery of 2 fixpoints. - tommy1729 - 05/03/2014
Hello tetration freaks ! Karlin and Mcgregor showed that: If is a function holomorphic and single valued on the complement of a closed countable set in the extended complex plane. Let two fixed points of such that and . Then the regular iterations at and are equal if and only if is a fractional linear function. [1] Karlin, S., & Mcgregor, J. ( 1968 ). Embedding iterates of analytic functions with two fixed points into continuous groups. Trans. Am. Math. Soc., 132, 137–145. However if is not true , can we have regular iterations that are independant of the fixpoint used ? regards tommy1729 |