Abstract.
The paper develops a technique for proving properties that are typical in the boundary of the connectedness locus with respect to the harmonic measure. A typical expansion condition along the critical orbit is proved. This condition implies a number of properties, including the Collet-Eckmann condition, Hausdorff dimension less than 2 for the Julia set, and the radial continuity in the parameter space of the Hausdorff dimensions of totally disconnected Julia sets.
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Oblatum 6-XI-1998 & 12-V-2000¶Published online: 11 October 2000
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Graczyk, J., Świątek, G. Harmonic measure and expansion on the boundary of the connectedness locus. Invent. math. 142, 605–629 (2000). https://doi.org/10.1007/s002220000100
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DOI: https://doi.org/10.1007/s002220000100