Hausdorff dimension of Cantor attractors in one-dimensional dynamics

• 成果类型: Article
• 署名作者: Li, Simin; Shen, Weixiao
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0083-9
• 发表日期: 2008
• 页码: 345-387
• 关键词: negative schwarzian; MAPS

摘要

In this paper, we study the Hausdorff dimension of Cantor attractors of smooth interval maps with non-flat critical points. We prove that the Hausdorff dimension is bounded from above by a constant less than 1 which depends only on the number and order of the critical points.