Sharp Lipschitz constant of bi-Lipschitz automorphism on Cantor set

【摘要】 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 -1 2 -r) 2(r13 + - r r +4 r2) , where lip(g) = supx,y∈Cr, x=y |g(x|x)--yg(| y)|and blip(g) = max(lip(g), lip(g-1)).更多还原

【Abstract】 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 -1 2 -r) 2(r13 + - r r +4 r2) , where lip(g) = supx,y∈Cr, x=y |g(x|x)--yg(| y)|and blip(g) = max(lip(g), lip(g-1)).更多还原