Harmonic measure and expansion on the boundary of the connectedness locus
Jacek Graczyk , Grzegorz Świątek
AbstractThe 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.
|Journal series||Inventiones Mathematicae, ISSN 0020-9910|
|Publication size in sheets||1.2|
|Keywords in English||Hausdorff Dimension; Harmonic Measure; Connectedness Locus; External Argument; External Radius|
|Publication indicators||= 20; = 19; = 27.0; : 2000 = 2.843; : 2006 = 1.659 (2) - 2007=1.929 (5)|
|Citation count*||27 (2015-08-08)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.