On arithmetic sums of fractal sets in \Bbb R^d

2020/06/22 by De‐Jun Feng, Yufeng Wu, FENG, De-Jun +1 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Primary 28A75 Secondary 28A80

paper · pdf · doi:10.48550/arxiv.2006.12058

openalex publication_date 2020/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A compact set E⊂ \Bbb R^d is said to be arithmetically thick if there exists a positive integer n so that the n-fold arithmetic sum of E has non-empty interior. We prove the arithmetic thickness of E, if E is uniformly non-flat, in the sense that there exists ε₀>0 such that for x∈ E and 0

Citations

• Fractal Geometry: Mathematical Foundations and Applications.
• Matrix semigroups with constant spectral radius

Cited by

• A nonlinear version of the Newhouse thickness theorem

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