Lipschitz Equivalence of Self-similar Sets Satisfying the Open Set Condition

摘要

Fix r ∈ (0,1) and an integer N ≥ 2. Let E and E' be self-similar sets generated by N contraction mappings of the form S(x) = ±rx + b. Suppose that open set conditions hold for E and E', where the corresponding open sets are open intervals, then E and E' are Lipschitz equivalent.