 Nem(z)=z+z^3+qz^4 - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Computation (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=8) +--- 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.