• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Polygon cyclic fixpoint conjecture tommy1729 Ultimate Fellow Posts: 1,491 Threads: 355 Joined: Feb 2009 05/17/2016, 12:28 PM (This post was last modified: 05/18/2016, 12:21 PM by tommy1729.) Consider a real-analytic function f. Consider An nth cyclic fixpoint A. N >= 4. Connect those n fixpoints : A , f(A) , ... With a straith line. That makes a polygon. Consider the cyclic points that make convex polygons. Call them convex cyclic points. Call the polygons : cyclic polygons. Conjecture : Every cyclic polygon within a cyclic polygon of order n , is cyclic of order m : M =< N. Regards Tommy1729 tommy1729 Ultimate Fellow Posts: 1,491 Threads: 355 Joined: Feb 2009 05/18/2016, 12:26 PM (05/17/2016, 12:28 PM)tommy1729 Wrote: Consider a real-analytic function f. Consider An nth cyclic fixpoint A. N >= 4. Connect those n fixpoints : A , f(A) , ... With a straith line. That makes a polygon. Consider the cyclic points that make convex polygons. Call them convex cyclic points. Call the polygons : cyclic polygons. Conjecture : Every cyclic polygon within a cyclic polygon of order n , is cyclic of order m : M =< N. Regards Tommy1729 I assume there are conditions that we need to add. True for all f would be surprising. I guess it is more of An intresting property than conjecture. And a quest for examples and counterex. Is it true for f = exp ?? Also , is every 2cycle close to a fixpoint for exp ? I guess so. Regards Tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post conjecture 666 : exp^[x](0+si) tommy1729 2 745 05/17/2021, 11:17 PM Last Post: tommy1729 Iteration exercises: f(x)=x^2 - 0.5 ; Fixpoint-irritation... Gottfried 23 51,719 10/20/2017, 08:32 PM Last Post: Gottfried @Gottfried : answer to your conjecture on MSE. tommy1729 2 5,654 02/05/2017, 09:38 PM Last Post: Gottfried (Again) fixpoint outside Period tommy1729 2 5,379 02/05/2017, 09:42 AM Last Post: tommy1729 The " outside " fixpoint ? tommy1729 0 2,850 03/18/2016, 01:16 PM Last Post: tommy1729 Natural cyclic superfunction tommy1729 3 6,189 12/08/2015, 12:09 AM Last Post: tommy1729 Cyclic dynamics f(-x) = T (f(x)) tommy1729 2 5,018 08/25/2015, 08:23 AM Last Post: tommy1729 2015 Continuum sum conjecture tommy1729 3 6,684 05/26/2015, 12:24 PM Last Post: tommy1729 Conjecture on semi-exp base change [2015] tommy1729 0 3,235 03/24/2015, 03:14 PM Last Post: tommy1729 2 fixpoint pairs [2015] tommy1729 0 3,189 02/18/2015, 11:29 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)