Lipschitz constant for bi-Lipschitz automorphism on Moran-like sets

摘要

This paper proves that if F subset of R-1 is a complete set equipped with some suitable Moran-like structure, then there is a constant c(0) > I such that for any bi-Lipschitz bijection f : F -> F, blip(f) = 1 or blip(f) >= c(0), where lip(g) = sup(x not equal y) vertical bar g(x)-g(y)vertical bar/vertical bar x-y vertical bar and blip(g) = max{lip(g), lip(g(-1))}. (c) 2007 Elsevier Inc. All rights reserved.