02/13/2015, 02:25 AM

(02/13/2015, 12:45 AM)tommy1729 Wrote: Im fascinated by the (subset) Taylor(x,ln(x)) (or transseries if you want) used for the parabolic fixpoint.Thank you for your interest, tommy1729.

Its ring structure makes solving the zoom equation ( F(f(x)) = f(ax) ) natural.

( polynomials of Taylor(x,ln(x)) are of same type and also Taylor(ax,ln(ax)) is of same type ! )

This needs more attention imho. ..

Have you write some similar expansions? Do they work?

Quote:Are all parabolic fixpoint expansions (for iterating analytic functions) like this ??I think so. You may compare it to expansion of superfunction of transferfunction zex(z)=z exp(z)

It is described in chapter 12 of book "Суперфункции".

The Mathematica code to caluate the expansion is suggested in section 12.2.

Quote:.. what about terms ln(x)^7 x^3 then ?You may extract the coefficient from the C++ implementation at

http://mizugadro.mydns.jp/t/index.php/E1etf.cin

Best regard, Dmitrii