On mappings of self-similar curves

In 197S D. Ivascu, a Roumanian mathematician, introduced the concept of a free quasisym-metry from axis $\mathbb{R}$ onto itself. The class of homogeneous mappings under study in the article generalizes the concept for topological embeddings of arbitrary subsets of the space $\mathbb{R}^n$. We prove existence of a homogeneous mapping from a segment onto a Koch curve which implies existence of a one-parameter group of bi-Lipschitz homomorphisms of the Koch curve onto itself with a common Lipschitz constant.