This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D=(r_1D)∪(r_2D+(1+r_1-r_2-r_3)/2)∪(r_3D+1+r_3) and E=(r_1E)∪(r_2E+1-r_2- r_3)∪(r_3E+1-r_3),and proves that D and E are Lipschitz equivalent if and only if there are positive integers m and n such that r_1~m=r_3~n.
Li-feng XI~(1+) Huo-jun RUAN~2 1 Institute of Mathematics,Zhejiang Wanli University,Ningbo 315100,China
In this paper, we discuss the Lipschitz equivalence of self-similar sets with triangular pattern. This is a generalization of {1, 3, 5}-{1, 4, 5} problem proposed by David and Semmes. It is proved that if two such self-similar sets are totally disconnected, then they are Lipschitz equivalent if and only if they have the same Hausdorff dimension.
The notion of finite-type open set condition is defined to calculate the Hausdorff dimensions of the sections of some self-similar sets, such as the dimension of intersection of the Koch curve and the line x=α with α∈ Q.
