• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 The mystery of 2 fixpoints. tommy1729 Ultimate Fellow Posts: 1,358 Threads: 330 Joined: Feb 2009 05/03/2014, 10:11 PM (This post was last modified: 05/03/2014, 10:12 PM by tommy1729.) Hello tetration freaks ! Karlin and Mcgregor showed that: If $f$ is a function holomorphic and single valued on the complement of a closed countable set in the extended complex plane. Let $s_1\neq s_2$ two fixed points of $f$ such that $|f'(s_0)|,|f'(s_1)|\neq 0,1$ and $f([s_1,s_2])\subseteq [s_1,s_2]$. Then the regular iterations at $s_1$ and $s_2$ are equal if and only if $f$ 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 $f([s_1,s_2])\subseteq [s_1,s_2]$ is not true , can we have regular iterations that are independant of the fixpoint used ? regards tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Merged fixpoints of 2 iterates ? Asymptotic ? [2019] tommy1729 1 272 09/10/2019, 11:28 AM Last Post: sheldonison b^b^x with base 0 method of iteration series tommy1729 0 1,346 12/21/2016, 01:27 PM Last Post: tommy1729 2 fixpoints related by power ? tommy1729 0 1,342 12/07/2016, 01:29 PM Last Post: tommy1729 2 real fixpoints again ....... tommy1729 10 8,450 02/23/2016, 10:17 PM Last Post: tommy1729 Fixpoints a,b with f ' (a) = f ' (b) = 1 tommy1729 0 1,551 09/15/2015, 08:29 AM Last Post: tommy1729 alternative fixpoints = branches ? tommy1729 0 1,652 10/11/2014, 08:50 AM Last Post: tommy1729 Wild conjecture about 2 fixpoints. tommy1729 0 1,736 05/03/2014, 10:56 PM Last Post: tommy1729 Fixpoints of the dxp() - has there been discussion about it? Gottfried 0 2,057 11/10/2011, 08:29 PM Last Post: Gottfried conjecture 2 fixpoints tommy1729 3 4,193 08/15/2010, 07:08 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)