Precise asymptotics at the tip of the Mandelbrot set

Neil Dobbs, Jacek Graczyk, Nicolae Mihalache

For the quadratic family $f_c(z)=z^2+c$, the only parameters in the Mandelbrot set $\mathcal{M}$ for which the Julia set ${\mathcal{J}}_c$ has Hausdorff dimension $1$ are $c=0$ and $c=-2$. Nea…