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Periodic analytic iterations by Riemann mapping - Printable Version

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Periodic analytic iterations by Riemann mapping - tommy1729 - 03/02/2016

Let r denote riemann mapping.
r' denotes the functional inverse of r.

Let j be An analytic jordan curve around the origin.

R maps j to the unit circle.

Let r'(1) be the starting point A.

then iterations f^[x](r'(1)) with x > 0 ( real ) are periodic and analytic iff

F(z) = r' ( T ( r) ).
Where T is a complex number on the unit circle.

I think this is correct.

This seems to suggest exp has no periodIC iterational Jordan curve away from its fixpoints.

Regards

Tommy1729




RE: Periodic analytic iterations by Riemann mapping - tommy1729 - 03/05/2016

Strongly related

http://math.eretrandre.org/tetrationforum/showthread.php?tid=1038

Regards

Tommy1729