MATHEMATICAE

Area and Hausdorff dimension of the set of accessible points of the Julia sets of λez and λ sin z by Bogus lawa Ka rp i n ́ s k a (Warszawa) Abstract. The Julia set Jλ of the exponential function Eλ: z → λe z for λ ∈ (0, 1/e) is known to be a union of curves (“hairs”) whose endpoints Cλ are the only accessible points from the basin of attraction. We show that for λ as above the Hausdorff dimension of Cλ is equal to 2 and we give estimates for the Hausdorff dimension of the subset of Cλ related to a finite number of symbols. We also consider the set of endpoints for the sine family Fλ: z → (1/(2i))λ(e iz − e−iz) for λ ∈ (0, 1) and prove that it has positive Lebesgue measure