Abstract
The Julia set Jof the exponential function E� : z ! �e z for � 2 (0,1/e) is known to be a union of curves (hairs) whose endpoints Care the only accessible points from the basin of attraction. We show that foras above the Hausdorff dimension of Cis equal to 2 and we give estimates for the Hausdorff dimension of the subset of Crelated to a finite number of symbols. We also consider the set of endpoints for the sine family F� : z ! (1/(2i))�(e iz e iz ) for � 2 (0,1) and prove that it has positive Lebesgue measure.
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