Quasi-Lipschitz equivalence of fractals

The paper proves that if E and F are dust-like C-1 self-conformal sets with 0 < H-H(dim)E (E), H-H(dim)F (F) < infinity, then there exists a bijection f: E -> F such that (dim(H)F) log vertical bar f(x) - f(y)vertical bar/(dim(H)E) log vertical bar x -y vertical bar -> 1 uniformly as vertical bar x-y vertical bar -> 0. It is also proved that a self-similar arc is Hoder equivalent to [0, 1] if and only if it is a quasi-arc.