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Parabolic Iteration, again

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Parabolic Iteration, again
andydude Offline
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#12
05/14/2008, 02:56 AM (This post was last modified: 05/14/2008, 02:58 AM by andydude.)
bo198214 Wrote:There are no denominators depending on the value of any \( f_k \).

You're right about \( f_2=0 \), and I was wrong.
I was thinking of A. A. Bennett "The Iteration of Functions of one Variable" where he says (page 30)
Bennett Wrote:The only other cases which can arise are the singular ones, and in these, \( a_{11} = 0 \).
Which is refering to the Carleman matrix of a function with a fixed point at zero. So if \( f(0) = 0 \) and \( f'(0) = 0 \) then the Carleman matrix is not invertible (i.e. singular). This is completely different than what I remember reading, and it doesn't apply to \( f''(0) \) at all. This means that the case \( f''(0) = 0 \) is a singularity of my generating functions, and not a singularity of parabolic iteration.

Andrew Robbins
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Messages In This Thread
Parabolic Iteration, again - by andydude - 04/30/2008, 10:03 AM
RE: Parabolic Iteration, again - by Ivars - 04/30/2008, 10:19 AM
RE: Parabolic Iteration, again - by andydude - 04/30/2008, 04:30 PM
RE: Parabolic Iteration, again - by Ivars - 04/30/2008, 07:02 PM
RE: Parabolic Iteration, again - by andydude - 04/30/2008, 07:34 PM
RE: Parabolic Iteration, again - by andydude - 05/03/2008, 08:10 PM
RE: Parabolic Iteration, again - by bo198214 - 05/04/2008, 07:14 AM
RE: Parabolic Iteration, again - by andydude - 05/05/2008, 05:26 AM
RE: Parabolic Iteration, again - by andydude - 05/07/2008, 12:57 AM
RE: Parabolic Iteration, again - by andydude - 05/05/2008, 08:30 AM
RE: Parabolic Iteration, again - by bo198214 - 05/05/2008, 05:33 PM
RE: Parabolic Iteration, again - by andydude - 05/14/2008, 02:56 AM

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