seminar: Hausdorff dimension of biaccessible angles of quadratic Julia sets and of the Mandelbrot set
speaker: Henk Bruin (Universität Wien)abstract: For "most" parameters c on the boundary of the Mandelbrot set, the Julia set \(J_c\) of the corresponding quadratic polynomial \(z \mapsto z^2+c\) is a dendrite, that is, a one-dimensional, compact, connected, locally connected set without loops. A point\( z\) on this dendrite is biaccessible if the external ray of at least two different angles land on \(z\). By extension, we call an angle biaccessible if its ray lands together with the ray of another angle. In this joint work with Dierk Schleicher (Jacobs University Bremen), I want to present combinatorial methods to detect biaccessible angles, giving tools to estimate their Hausdorff dimension. Due to the local similarity between the Julia set \(J_c\) and the Mandelbrot set near \(c\), such methods can also be applied to the biaccessible angles in parameter space.
timetable:
Thu 23 Feb, 16:00 - 17:00, Sala Conferenze Centro De Giorgi
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