Harmonic measure and expansion on the boundary of the connectedness locus

• 成果类型: Article
• 署名作者: Graczyk, J; Swiatek, G
• 署名单位: Royal Institute of Technology; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220000100
• 发表日期: 2000
• 页码: 605-629
• 关键词: families

摘要

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.