SELF-SIMILAR SETSrecent resultsBernoulli convolutions problemWe report on recent results about the dimension and smoothness properties of self-similar sets and measures. Closely related to these are results on
Mathe, Self-similar and self-affine sets: measure of the intersection of two copies. Ergodic Theory Dynam. Systems 30 (2010), no. 2, 399-440. MR 2599886 Zbl 1200.28005M. Elekes, T. Keleti, and A. M´ath´e, Self-similar and self-affine sets; measures of the intersection of two...
Volume Doubling Measures and Heat Kernel Estimates on Self-Similar Sets (Memoirs of the American Mat 电子书 读后感 评分☆☆☆ 评分☆☆☆ 评分☆☆☆ 评分☆☆☆ 评分☆☆☆ 类似图书 点击查看全场最低价 出版者:American Mathematical Society 作者:Jun Kigami 出品人...
We prove under mild conditions that the set ofpoints with a unique coding can be identified with a subshift of finite type.As a consequence of this, we can show that the set of points with a uniquecoding is a graph-directed self-similar set in the sense of Mauldin andWilliams \\cite{...
We derive the formula for the 1-Wasserstein distance between a certain discrete approximation of self-similar measures associated to a pair of non-overlapping linear contraction of the unit interval [Math Processing Error]. We restrict our arguments to the case where the maps have the same contrac...
It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the weak separation property ...
CONNECTEDSELF-SIMILARSETS TAI-MANTANG Abstract.LetTbetheattractorofinjectivecontractionsf 1 ,...,f m on R 2 thatsatisfytheOpenSetCondition.IfTisconnected,∂Tisarcwise connected.Inparticular,theboundaryoftheL´evydragonisarcwisecon- nected. ...
Inthispaper,wepresentamoresimpleandmuchshorterproofforthemainresultinthepaper'Annegativeanswertoaconjectureontheself-similarsetssatisfyingtheopensetcondition',whichwaspublishedinthejournalAnalysisinTheoryandApplicationsin2009.
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Q. Li and Z.-Y. Wu, On spectral and non-spectral problem for the planar self-similar measures with four element digit sets, Forum Math. 33 (2021), no. 6, 1629–1639.10.1515/forum-2021-0173Search in Google Scholar [18]F. P. Ramsey, On a Problem of Formal Logic, Proc. Lond. Mat...