Posts: 151

Threads: 9

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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?

Posts: 633

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Joined: Oct 2008

02/06/2016, 11:06 PM
(This post was last modified: 02/06/2016, 11:08 PM by sheldonison.)
(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/...onvergence I have not seen the superfunction formal solution though.

- Sheldon

Posts: 151

Threads: 9

Joined: Apr 2008

(02/06/2016, 11:06 PM)sheldonison Wrote: http://mathoverflow.net/questions/45608/...onvergence 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.