 Polygon cyclic fixpoint conjecture - 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: Polygon cyclic fixpoint conjecture (/showthread.php?tid=1082) Polygon cyclic fixpoint conjecture - tommy1729 - 05/17/2016 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 RE: Polygon cyclic fixpoint conjecture - tommy1729 - 05/18/2016 (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