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Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets 被引量：11

Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets
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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.
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》 SCIE 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
关键词 SELF-SIMILAR set OVERLAP LIPSCHITZ EQUIVALENCE graph-directed construction ERGODICITY MARTINGALE self-similar set overlap Lipschitz equivalence graph-directed construction ergodicity martingale
分类号 O157.5 [理学—基础数学]
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参考文献14

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  • 2[2]David G,Semmes S.Fractured Fractals and Broken Dreams:Self-similar Geometry through Metric and Measure.Oxford:Oxford University Press,1997
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  • 4[4]Falconer K J,Marsh D T.On the Lipschitz equivalence of Cantor sets.Mathematika,39:223-233 (1992)
  • 5[5]Rao H,Ruan H J,Xi L F.Lipschitz equivalence of self-similar sets.C R Math Acad Sci Paris,342(2):191-196 (2006)
  • 6[6]Wen Z Y,Xi L F.Relations among Whitney sets,self-similar arcs and quasi-arcs.Israel J Math,136:251-267 (2003)
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同被引文献16

  • 1Chen X C,Xi L F.Quasi-Lipschitz equivalence on homogeneous uniform Moran sets. Acta Math Sinica (Chin Ser) . 2010
  • 2Mattila P,Saaranen P.Ahlfors-David regular sets and bilipschitz maps. Annales Academiae Scientiarum Fennicae Series A1 Mathematica . 2009
  • 3Xi L F,Xiong Y.Lipschitz equivalence of fractals generated by nested cubes. Mathematische Zeitschrift .
  • 4Falconer K J.Techniques in Fractal Geometry. . 1997
  • 5David G,Semmes S.Fractured Fractals and Broken Dreams:Self-similar Geometry through Metric and Measure. . 1997
  • 6Xi,L. F.Lipschitz equivalence of self-conformal sets. Journal of the London Mathematical Society . 2004
  • 7L.F. Xi.Quasi-Lipschitz equivalence of fractals. Israel Journal of Mathematics . 2007
  • 8Falconer K J,Marsh D T.On the Lipschitz equivalence of Cantor sets. Mathematika . 1992
  • 9Farb,B.,Mosher,L.A rigidity theorem for the solvable Baumslag–Solitar groups (With an appendix by Daryl Cooper). Inventiones Mathematicae . 1998
  • 10Xi L F,Xiong Y.Self-similar sets with initial cubic patterns. C R Math Acad Sci Paris . 2010

引证文献11

二级引证文献7

Science China Mathematics
2007年 第11期

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