Feliks Przytycki, Mariusz Urbanski, Anna Zdunik, Harmonic, Gibbs and Hausdorff Measures on Repellers for Holomorphic Maps, I, Annals of Mathematics, Second Series, Vol. 130, No. 1 (Jul., 1989), pp. 1-40
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Przytycki et al. (1989) studied this question.
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