B.O. Stratmann, M. Urbanski, M. Zinsmeister
Well-Approximable Points for Julia Sets with Parabolic and Critical Points
Preprint series: Mathematica Gottingensis

MSC:

30E99 None of the above but in this section

Abstract: We consider rational functions f with parabolic and critical points contained
in their Julia sets such that the derivative of the
iterates of f at all critical value tends to infinity.
We calculate the Hausdorff dimensions of subsets of the
Julia sets consisting of elements whose forward orbit avoids
a neighbourhood of the critical points and which are
well-approximable by backward iterates of parabolic periodic
points of f.


Keywords: Julia Sets, Critical Points, Conformal Measures, Diophantine Approximations