The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets

• 成果类型: Article
• 署名作者: Shishikura, M
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/121009
• 发表日期: 1998
• 页码: 225-267
• 关键词: rational maps; DYNAMICS; families

摘要

It is shown that the boundary of the Mandelbrot set M has Hausdorff dimension two and that for a generic c is an element of partial derivative M, the Julia set of z bar right arrow z(2) + c also has Hausdorff dimension two. The proof is based on the study of the bifurcation of parabolic periodic points.