🚀 go-pugleaf

In article <1992Nov8.234155.14813@mnemosyne.cs.du.edu> ddixon@nyx.cs.du.edu (David Dixon) writes:
>Is anybody aware of any differences between mappings with and without
>singular points?  For example, say I have a map x[n+1] = f(x[n]), where
>df/dx is singular at some point.  Does this show any behavior not seen
>in maps involving analytic functions?

I've done some experimenting with maps x[n+1] = x^(-n)+C.  The main
difference I noted with this map is that the map doesn't diverge to
infinity.  (I.e. infinity gets mapped back C, as opposed to the mandelbrot
set, where infinity is mapped to infinity.)

I guess rational polynomial functions (i.e. P(x)/Q(x)) have singular points.
Their behavior isn't very different from polynomial functions, although
there are a few differences (I can't remember the details).

A good reference for rational polynomial fractals is:
%T Complex Analytic Dynamics on the Riemann Sphere
%A P. Blanchard
%J Bull. of the Amer. Math. Soc
%V 11
%N 1
%D July 1984
%P 85-141

(I highly recommend that paper for anyone interested in the mathematical
side of fractals.)

Ken Shirriff				shirriff@sprite.Berkeley.EDU