Polygon cyclic fixpoint conjecture tommy1729 Ultimate Fellow Posts: 1,906 Threads: 409 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: 1,906 Threads: 409 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 »

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