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+--- Thread: Nem(z)=z+z^3+qz^4 (/showthread.php?tid=1054)
Nem(z)=z+z^3+qz^4 - Kouznetsov - 02/06/2016
Hello, colleagues.
I have constructed superfunction and abelfnction for the polynomial of special kind, Nem(z)=z+z^3+qz^4,
where q is positive parameter.
I load the description as
http://mizugadro.mydns.jp/2016NEMTSOV/TRY00/23.pdf
Dmitrii Kouznetsov.
Nemtsov function and its iterates.
2016, in preparation.
http://mizugadro.mydns.jp/t/index.php/Nemtsov_function
Could anybody criticise it?
RE: Nem(z)=z+z^3+qz^4 - sheldonison - 02/06/2016
(02/06/2016, 01:41 PM)Kouznetsov Wrote: Hello, colleagues.
I have constructed superfunction and abelfnction for the polynomial of special kind, Nem(z)=z+z^3+qz^4,
where q is positive parameter.
I load the description as
http://mizugadro.mydns.jp/2016NEMTSOV/TRY00/23.pdf
Dmitrii Kouznetsov.
Nemtsov function and its iterates.
2016, in preparation.
http://mizugadro.mydns.jp/t/index.php/Nemtsov_function
Could anybody criticise it?
Dimitrii,
This is an example of the parabolic case. There are some links on MSE to the fractional iterates for sin(x), which is a similar problem. In general, the Abel function and the fractional iterates are well known, and have a formal asymptotic series which turns out to have a zero radius of convergence. For example; see http://mathoverflow.net/questions/45608/formal-power-series-convergence I have not seen the superfunction formal solution though.
RE: Nem(z)=z+z^3+qz^4 - Kouznetsov - 02/07/2016
(02/06/2016, 11:06 PM)sheldonison Wrote: http://mathoverflow.net/questions/45608/formal-power-series-convergence I have not seen the superfunction formal solution though.Thank you, sheldonison. I add the link you suggest to article
http://mizugadro.mydns.jp/t/index.php/Sin
Superfunction for sin is described in
http://mizugadro.mydns.jp/t/index.php/SuSin
http://mizugadro.mydns.jp/PAPERS/2014susin.pdf D.Kouznetsov. Super sin. Far East Jourmal of Mathematical Science, v.85, No.2, 2014, pages 219-238.