• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 The " outside " fixpoint ? tommy1729 Ultimate Fellow Posts: 1,491 Threads: 355 Joined: Feb 2009 03/18/2016, 01:16 PM Im thinking about real-entire functions , strictly increasing on the reals such that 1) they have no real fixpoint , nor at +\- oo. ( -oo is fixpoint of exp(z) + z , but x^2 does not have + oo as fixpoint although oo^2 = oo ; x^2 is not asymp to id(x) ). 2) in the univalent zone near the real axis where f maps univalent to all of C or C\y ( single value y ) , f has no fixpoint. Equivalent f^[-1](x) , the branch near the real line , has no fundamental fixpoints. So the fixpoints of f resp Inv f must lie outside the zone resp branch. I call them " outside " fixpoints. This makes me wonder about the super of f. Clearly the outside fixpoints make the super way different. For instance no fixpioints at + oo i like sexp has. Reminds me a bit of secondary fixpoint methods. Not sure what the most intresting f would be. I assume the simplest topology for the zone comes first. ; no holes for instance. Notice b^z always has " inside fixpoints " for b > eta. A theory for these outside fix would be Nice too ! Regards Tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread The " outside " fixpoint ? - by tommy1729 - 03/18/2016, 01:16 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Iteration exercises: f(x)=x^2 - 0.5 ; Fixpoint-irritation... Gottfried 23 52,095 10/20/2017, 08:32 PM Last Post: Gottfried (Again) fixpoint outside Period tommy1729 2 5,413 02/05/2017, 09:42 AM Last Post: tommy1729 Polygon cyclic fixpoint conjecture tommy1729 1 4,443 05/18/2016, 12:26 PM Last Post: tommy1729 2 fixpoint pairs [2015] tommy1729 0 3,206 02/18/2015, 11:29 PM Last Post: tommy1729 [2014] The secondary fixpoint issue. tommy1729 2 6,348 06/15/2014, 08:17 PM Last Post: tommy1729 Simple method for half iterate NOT based on a fixpoint. tommy1729 2 6,272 04/30/2013, 09:33 PM Last Post: tommy1729 2 fixpoint failure tommy1729 1 4,700 11/13/2010, 12:25 AM Last Post: tommy1729 abs f ' (fixpoint) = 0 tommy1729 2 7,277 09/09/2010, 10:13 PM Last Post: tommy1729 [Regular tetration] [Iteration series] norming fixpoint-dependencies Gottfried 11 22,957 08/31/2010, 11:55 PM Last Post: tommy1729 the inconsistency depending on fixpoint-selection Gottfried 27 43,470 04/29/2008, 08:15 AM Last Post: bo198214

Users browsing this thread: 1 Guest(s)