02/13/2015, 12:45 AM

Im fascinated by the (subset) Taylor(x,ln(x)) (or transseries if you want) used for the parabolic fixpoint.

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.

Are all parabolic fixpoint expansions (for iterating analytic functions) like this ??

what about terms ln(x)^7 x^3 then ?

regards

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.

Are all parabolic fixpoint expansions (for iterating analytic functions) like this ??

what about terms ln(x)^7 x^3 then ?

regards

tommy1729