Sharp Lipschitz constant of bi-Lipschitz automorphism on Cantor set

• 作 者: Ying Xiong (1) LiSha Wang
• 机 构: 1.DepartmentofMathematics,2.DepartmentofMathematics,3.InstituteofMathematics
• 出 处: 中国科学：数学英文版
• 发表日期: 2009年4期
• 关键词: FRACTAL bi-Lipschitz AUTOMORPHISM CANTOR set fractal bi-Lipschitz automorphism C
• 基金项目: supported by National Natural Science Foundation of China (Grant Nos. 10671180, 10571140,10571063, 10631040, 11071164),Morningside Center of Mathematics

Suppose Cr = (rCr) ∪ (rCr + 1 - r) is a self-similar set with r ∈ (0, 1/2), and Aut(Cr) is the set of all bi-Lipschitz automorphisms on Cr. This paper proves that there exists f* ∈ Aut(Cr) such that blip(f*) = inf{blip(f) 】 1 : f ∈ Aut(Cr)} = min 1r , (1