Quote:
Originally Posted by Qfwfq
OK when saying "the" Mandelbrot set we usually mean "that" one i. e. the one given by the form  so the relation is with the quadratic Julia sets. As for the map, it's definitely surjective over the quadatic Julia sets, by definition, so if the map is injective then it's also bijective.  |
Like you, I don't know if Mandelbrot ever considered other analytic functions as being claim to being the set named after him or just referring to only quadratic function. As for the rest, I defer to your more concise definition. My Analysis course (injective + surjective = bijective) is a bit rusty.
I will admit I am always thinking in the largest of terms by using the largest container.
I conjectured a long time ago that an Iterative Function System f(z) can be formed from any analytic function being defined over a piecewise continuous domain.
maddog
