08/08/2009, 11:31 PM
ok , first i dont know if this has been asked or answered before , so forgive my ignorance if such is the case.
consider an analytic function f(z) , strictly rising on the reals with 2 real fixpoints.
now we can use regular iteration for each fixpoint and thus get two ' zones ' that are ' correct ' half-iterates. ( assuming radius = oo too )
sketch :
[ - oo .. zone 1 .. fixpoint 1 .. zone 2 .. fixpoint 2 .. zone 3 .. + oo ]
when expanded at fixpoint 1 and missing the fixpoint 2 ( and radius oo ) i consider that regular half-iterate as a correct solution to 'zone 1'
similarly :
when expanded at fixpoint 2 and missing the fixpoint 1 ( and radius oo ) i consider that regular half-iterate as a correct solution to 'zone 3'
So the question becomes , what gives zone 2 ?
Regards
Tommy1729
consider an analytic function f(z) , strictly rising on the reals with 2 real fixpoints.
now we can use regular iteration for each fixpoint and thus get two ' zones ' that are ' correct ' half-iterates. ( assuming radius = oo too )
sketch :
[ - oo .. zone 1 .. fixpoint 1 .. zone 2 .. fixpoint 2 .. zone 3 .. + oo ]
when expanded at fixpoint 1 and missing the fixpoint 2 ( and radius oo ) i consider that regular half-iterate as a correct solution to 'zone 1'
similarly :
when expanded at fixpoint 2 and missing the fixpoint 1 ( and radius oo ) i consider that regular half-iterate as a correct solution to 'zone 3'
So the question becomes , what gives zone 2 ?
Regards
Tommy1729