Projections of Self-Similar and Related Fractals: A Survey of Recent Developments
Projections of Self-Similar and Related Fractals: A Survey of Recent Developments
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自相似和相关分形的预测：近期发展调查
DOI：
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发表时间：
2015
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通讯作者：
Pablo Shmerkin
中科院分区：
文献类型：
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作者：
Pablo Shmerkin
近年来，人们对理解许多具体分形集和测度的预测产生了很大兴趣并取得了很大进展。总体目标是能够超越马斯特兰德定理等一般结果，并量化每个投影的大小——或者至少量化某个非常小的集合之外的每个投影。本文调查了其中一些结果以及为获得这些结果而开发的技术，重点关注平面自相似集和测度的线性投影。
In recent years there has been much interest -and progress- in understanding projections of many concrete fractals sets and measures. The general goal is to be able to go beyond general results such as Marstrand’s Theorem, and quantify the size of every projection – or at least every projection outside some very small set. This article surveys some of these results and the techniques that were developed to obtain them, focusing on linear projections of planar self-similar sets and measures.