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11/13/2007, 10:36 AM
(This post was last modified: 11/13/2007, 10:37 AM by bo198214.)
jaydfox Wrote:Do you mean that the function being iterated is entire,

Exactly.

Quote:For example, multiplication is entire, as is exponentiation (the continous iterator).

However multiplication

has only one fixed point, so the theorem can not apply.

Quote: However, exponentiation is entire,

And thatswhy the

can not be the same at any two fixed points. Thatswhy the

at one fixed point has singularities at all other fixed points. Every Abel function of an entire function has singularities at every fixed point except at most 1.

Quote:Edit: Since he just left (or is about to leave) on a 2-month trip,

Its my last day, I rather should be occupied with packing