Harmonic measure and expansion on the boundary of the connectedness locus

Jacek Graczyk , Grzegorz Świątek

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.
Author Jacek Graczyk - [The Royal Institute of Technology (KTH)]
Jacek Graczyk,,
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, Grzegorz Świątek (FMIS / DFE)
Grzegorz Świątek,,
- Department of Functional Equations
Journal seriesInventiones Mathematicae, ISSN 0020-9910
Issue year2000
Vol142
No3
Pages605-629
Publication size in sheets1.2
Keywords in EnglishHausdorff Dimension; Harmonic Measure; Connectedness Locus; External Argument; External Radius
ASJC Classification2600 General Mathematics
DOIDOI:10.1007/s002220000100
URL https://link.springer.com/article/10.1007/s002220000100
Languageen angielski
Score (nominal)50
Score sourcejournalList
Publication indicators Scopus Citations = 20; WoS Citations = 19; GS Citations = 27.0; Scopus SNIP (Source Normalised Impact per Paper): 2000 = 2.843; WoS Impact Factor: 2006 = 1.659 (2) - 2007=1.929 (5)
Citation count*27 (2015-08-08)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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