Projections of self-similar and related fractals: a survey of recent developments

2015/01/05 by Pablo Shmerkin, Shmerkin, Pablo · 1 citation
Mathematics · Physics and Astronomy · #28A80 #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary: 28A78 #Secondary: 37A99 #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1501.00875

openalex publication_date 2015/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• The Hausdorff dimension of the intersection of ψ-well approximable numbers and self-similar sets

Related

• Statistically self-similar fractal sets
• Sixty Years of Fractal Projections
• Projections of self-affine fractals
• Estimate of the Hausdorff Dimension of a Self-Similar Set due to Weak Contractions
• Perturbation of self-similar sets and some regular configurations and comparison of fractals