Geography of the cubic connectedness locus I: Intertwining surgery

Details Geography of the cubic connectedness locus I: Intertwining surgery Geography of the cubic connectedness locus I: Intertwining surgery

1996-08-15

arxiv.org/abs/math/9608213v1

Mathematics

Dynamical Systems

Scientific paper

We exhibit products of Mandelbrot sets in the two-dimensional complex parameter space of cubic polynomials. These products were observed by J. Milnor in computer experiments which inspired Lavaurs' proof of non local-connectivity for the cubic connectedness locus. Cubic polynomials in such a product may be renormalized to produce a pair of quadratic maps. The inverse construction is an {\it intertwining surgery} on two quadratics. The idea of intertwining first appeared in a collection of problems edited by Bielefeld. Using quasiconformal surgery techniques of Branner and Douady, we show that any two quadratics may be intertwined to obtain a cubic polynomial. The proof of continuity in our two-parameter setting requires further considerations involving ray combinatorics and a pullback argument.

Affiliated with

Also associated with

No associations

Rating

Geography of the cubic connectedness locus I: Intertwining surgery does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geography of the cubic connectedness locus I: Intertwining surgery, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geography of the cubic connectedness locus I: Intertwining surgery will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-573039