Julia sets in the Mandelbrot set and small Mandelbrot sets

Date
2015/11/20 Fri 14:00 - 17:00
Room
6号館609号室
Speaker
Masashi Kisaka
Affiliation
Kyoto University
Abstract

If we zoom in a certain part of the Mandelbrot set, we can see a figure J' which is very similar to a certain Julia set. Furthermore, as we zoom in the middle part of J', we can see a certain nested structure which is
similar to the iterated preimages of J' by z^2 and finally a small Mandelbrot set M' appears. We explain how to formulate this phenomena and show that this actually occurs. Also we show that this kind of nested structure exists in J_c for c in M'.