Hausdorff dimension of biaccessible angles for quadratic polynomials
Volume 238 / 2017
Fundamenta Mathematicae 238 (2017), 201-239
MSC: Primary 37F20; Secondary 37B10, 37E25, 37E45, 37F50.
DOI: 10.4064/fm276-6-2016
Published online: 10 May 2017
Abstract
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.
