Hausdorff dimension of biaccessible angles for quadratic polynomials
A point $c$ in the Mandelbrot set is called biaccessible if two parameter rays land at $c$. Similarly, a point $x$ in the Julia set of a polynomial $z \mapsto z^2+c$ is called biaccessible if two dynamic rays land at $x$. In both cases, we say that the external angles of these two rays are biaccessible as well.
We describe a purely combinatorial characterization of biaccessible (both dynamic and parameter) angles, and use it to give detailed estimates of the Hausdorff dimension of the set of biaccessible angles.