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Real and complex behaviour of the base change function (was: The "cheta" function)
#23
(08/17/2009, 12:07 PM)jaydfox Wrote: In theory, most of the principles should be the same. The trivial singularities would be at all branched locations of log^[n-2](1) instead of of log^[n-2](-1), if I'm thinking this through correctly (which I might not be, it's 4 AM here and I just got up to give someone a lift to the airport).

We can use my formula above (which presents the by without branching induced singularities)


and apply it to and .
As is a fixed point of we get and have the singularities
while the opposite base conversion has the by Jay determined singularities .

Here we have the interesting case that the singularities should converge to with increasing , i.e. a real instead of a non-real fixed point. I am however not sure about the behaviour for increasing and hope Jay makes some illustrating pictures Smile
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RE: Real and complex behaviour of the base change function (was: The "cheta" function) - by bo198214 - 08/17/2009, 02:40 PM

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