Harmonic measure and expansion on the boundary of the connectedness locus |
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| Authors: | Jacek Graczyk Grzegorz Świątek |
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| Affiliation: | (1) Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden, SE;(2) Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA, US |
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| 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. Oblatum 6-XI-1998 & 12-V-2000?Published online: 11 October 2000 |
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