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

This paper proves that if F⊂R1F⊂R1 is a complete set equipped with some suitable Moran-like structure, then there is a constant c0>1c0>1 such that for any bi-Lipschitz bijection f:F→F,blip(f)=1orblip(f)⩾c0, where lip(g)=supx≠y|g(x)−g(y)||x−y| and blip(g)=max{lip(g),lip(g−1)}blip(g)=max{lip(g),lip(g−1)}.