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Lipschitz equivalence of self-similar sets with touching structures
- Publication Year :
- 2012
-
Abstract
- Lipschitz equivalence of self-similar sets is an important area in the study of fractal geometry. It is known that two dust-like self-similar sets with the same contraction ratios are always Lipschitz equivalent. However, when self-similar sets have touching structures the problem of Lipschitz equivalence becomes much more challenging and intriguing at the same time. So far the only known results only cover self-similar sets in $\bR$ with no more than 3 branches. In this study we establish results for the Lipschitz equivalence of self-similar sets with touching structures in $\bR$ with arbitrarily many branches. Key to our study is the introduction of a geometric condition for self-similar sets called {\em substitutable}.<br />Comment: 30 pages, 4 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1207.6674
- Document Type :
- Working Paper