Half-iterate exp(z)-1: hypothese on growth of coefficients

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Half-iterate exp(z)-1: hypothese on growth of coefficients

Leo.W

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#46

08/28/2022, 01:41 PM

(08/19/2022, 06:26 PM)bo198214:The Julia function is considered as a formal powerseries here. The coefficients recursively obtained from the above equation are unique if we set \(j_k="0\) for \(k< m\) and" \(j_m="f_m\) where \(f(z) = z + f_m z^m + f_{m+1} z^{m+1}+ ...,\quad f_m\neq 0\). There is no theta-ambiguity here - like with the regular iteration at a fixed point. For parabolic iteration the condition is that the iterates are asymptotically analytic at the fixed point. Wrote: Oh! I see! now I think I'm dumb

(08/19/2022, 04:36 AM)Leo.W Wrote:
bo198214 Wrote:But the normal thing is that these Abel-Functions/Fatou-Coordinates are different from each other (and hence the iterates). Only in exceptional cases (e.g. LFTs) they agree.
Please lemme know what is this and why~
Its written in Milnor "Dynamics in one complex variable"
And btw I can not read your quotes when you use [size=1]!

Thanks, I read this book last year and obviously I skipped this chapter or sth...
How? I just tapped the "quote" button in chrome? Can't it load in mobiles? lol I'll be careful next time

Regards, Leo Smile

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Messages In This Thread

Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 07/19/2022, 08:11 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by MphLee - 07/19/2022, 09:40 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 07/19/2022, 10:19 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by MphLee - 07/21/2022, 12:15 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 07/21/2022, 01:13 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by MphLee - 07/21/2022, 02:18 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 07/20/2022, 10:49 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 07/21/2022, 07:30 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 07/22/2022, 01:44 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 07/22/2022, 02:57 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 07/24/2022, 02:23 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by tommy1729 - 08/06/2022, 09:56 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 08/07/2022, 09:19 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by tommy1729 - 08/06/2022, 10:14 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/07/2022, 09:51 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/10/2022, 02:12 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/11/2022, 03:28 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/11/2022, 07:03 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 08/11/2022, 01:26 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by tommy1729 - 08/12/2022, 01:47 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/15/2022, 05:24 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/18/2022, 04:48 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/18/2022, 11:37 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/18/2022, 06:25 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/19/2022, 04:36 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/19/2022, 06:26 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/28/2022, 01:41 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/28/2022, 03:45 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/29/2022, 05:05 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/18/2022, 08:01 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by tommy1729 - 08/18/2022, 12:17 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by bo198214 - 08/18/2022, 07:05 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Gottfried - 08/18/2022, 07:44 PM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/19/2022, 05:12 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/19/2022, 05:24 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/19/2022, 05:35 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/19/2022, 05:54 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/19/2022, 06:17 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/19/2022, 06:54 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by JmsNxn - 08/19/2022, 07:05 AM

RE: Half-iterate exp(z)-1: hypothese on growth of coefficients - by Leo.W - 08/19/2022, 07:57 AM

RE: Parabolic Formal Powerseries - by tommy1729 - 09/09/2022, 12:24 AM

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