On the interior of projections of planar self-similar sets

2018/07/31 by Yuki Takahashi, Takahashi, Yuki
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1807.11801

openalex publication_date 2018/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider projections of planar self-similar sets, and show that one can create nonempty interior in the projections by applying arbitrary small perturbations, if the self-similar set satisfies the open set condition and has Hausdorff dimension greater than 1.

Citations

• The Hausdorff dimension of the projections of self-affine carpets
• Projecting the one-dimensional Sierpinski gasket

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