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

This paper proves that if F ⊂ R1 is a complete set equipped with some suitable Moran-like structure, then there is a constant c0 > 1 such that for any bi-Lipschitz bijection f :F →F, blip(f ) =1 or blip(f ) c0, where lip(g) = supx =y |g(x)−g(y)| |x−y| and blip(g) = max{lip(g), lip(g−1)}. © 2007 Elsevier Inc. All rights reserved.