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