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The mystery of 2 fixpoints. - Printable Version

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The mystery of 2 fixpoints. - tommy1729 - 05/03/2014

Hello tetration freaks !

Karlin and Mcgregor showed that:

If is a function holomorphic and single valued on the complement of a closed countable set in the extended complex plane. Let two fixed points of such that and . Then the regular iterations at and are equal if and only if is a fractional linear function.

[1] Karlin, S., & Mcgregor, J. ( 1968 ). Embedding iterates of analytic functions with two fixed points into continuous groups. Trans. Am. Math. Soc., 132, 137–145.

However if is not true , can we have regular iterations that are independant of the fixpoint used ?