Local connectivity of the Mandelbrot set at certain infinitely renormalizable points

Details Local connectivity of the Mandelbrot set at certain infinitely renormalizable points Local connectivity of the Mandelbrot set at certain infinitely renormalizable points

1995-08-04

arxiv.org/abs/math/9508212v1

Mathematics

Dynamical Systems

Scientific paper

We construct a subset of the Mandelbrot set which is dense on the boundary
of the Mandelbrot set and which consists of only infinitely renormalizable
points such that the Mandelbrot set is locally connected at every point of
this subset. We prove the local connectivity by finding bases of connected
neighborhoods directly.

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