Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets  

作　　者：Li-feng XI~(1+) Huo-jun RUAN~2 1 Institute of Mathematics,Zhejiang Wanli University,Ningbo 315100,China 2 Department of Mathematics,Zhejiang University,Hangzhou 310027,China 

出　　处：《Science China Mathematics》2007年第11期1537-1551,共15页中国科学：数学（英文版）

基　　金：This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10301029,10671180,10601049) and Morningside Center of Mathematics

摘　　要：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.This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D = (r1D) ∪ (r2D + (1 + r1 - r2 - r3)/2) ∪ (r3D + 1 - r3) and E = (r1E) ∪ (r2E + 1 - r2 -r3) ∪ (r3E + 1 - r3),and proves that D and E areLipschitz equivalent if and only if there are positive integers m and n such that rm1= rn3.

关 键 词：SELF-SIMILAR set OVERLAP LIPSCHITZ EQUIVALENCE graph-directed construction ERGODICITY MARTINGALE 

分 类 号：O157.5[理学—数学]