Lipschitz Equivalence Of Self-similar Sets On Plane

In this paper, we mainly discuss the lipschitz equivalence of self-similar sets on plane by the graph-directed structure. In section 1, we make a general description on the recent researches in our field and the questions that we are concerned about and give the main results that we have acquired; In section 2, we mainly introduce the preliminaries for the paper; In section 3, we mainly study the shift space and the relation of shift space and attractor; In the section 4, we mainly study the Lipschitz equivalence of dust-like graph-directed sets; In the section 5, we proof the main results of the paper.