Submitted by ims_edit on Fri, 02/05/2021 - 13:19
preprint-id:
ims18-03
preprint-title:
Local connectivity of the Mandelbrot set at some satellite parameters of bounded type
preprint-abstract:
We explore geometric properties of the Mandelbrot set M, and the corresponding Julia sets J_c, near the main cardioid. Namely, we establish that: a) M is locally connected at certain infinitely renormalizable parameters c of bounded satellite type, providing first examples of this kind; b) The Julia sets J_c are also locally connected and have positive area; c) M is self-similar near Siegel parameters of constant type. We approach these problems by analyzing the unstable manifold of the pacman renormalization operator constructed in [DLS] as a global transcendental family.
preprint-year:
2018