Institute for Mathematical Sciences
External rays and the real slice of the mandelbrot set
Abstract: This paper investigates the set of angles of the parameter rays which land on the real slice [-2, 1/4] of the Mandelbrot set. We
prove that this set has zero length but Hausdorff dimension 1.
We obtain the corresponding results for the tuned images of the
real slice. Applications of these estimates in the study of
critically non-recurrent real quadratics as well as biaccessible
points of quadratic Julia sets are given.
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