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+--- 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