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 Parabolic Iteration, again andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 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 « Next Oldest | Next Newest »

 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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