Sums of two homogeneous Cantor sets

DOI10.1090/tran/7649zbMath1414.28009arXiv1710.10066OpenAlexW2963763197MaRDI QIDQ4967309

Yuki Takahashi

Publication date: 3 July 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.10066

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Fractals (28A80)

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Cites Work

• Unnamed Item
• There are no \(C^{1}\)-stable intersections of regular Cantor sets
• On self-similar sets with overlaps and inverse theorems for entropy
• The Lebesgue measure of the algebraic difference of two random Cantor sets
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Intersecting random translates of invariant Cantor sets
• On the measure of arithmetic sums of Cantor sets
• On the arithmetic difference of middle Cantor sets
• Convolutions of Cantor measures without resonance
• Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions
• Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian
• The algebraic difference of two random Cantor sets: the Larsson family
• On the exceptional set for absolute continuity of Bernoulli convolutions
• Stable intersections of affine Cantor sets
• On the sum and product of continued fractions
• Absolute continuity of self-similar measures, their projections and convolutions
• Projections of Self-Similar and Related Fractals: A Survey of Recent Developments
• Stable intersection of middle-α Cantor sets
• On sums of nearly affine Cantor sets
• When Cantor Sets Intersect Thickly
• On the structure of arithmetic sums of Cantor sets with constant ratios of dissection
• Resonance between Cantor sets
• Intersections of thick Cantor sets
• Self-similar measures and intersections of Cantor sets
• Sums of Cantor sets whose sum of dimensions is close to 1
• On the topology of arithmetic sums of regular Cantor sets
• Absolute continuity of Bernoulli convolutions for algebraic parameters
• Random intersections of thick Cantor sets
• Cantor sets and numbers with restricted partial quotients
• On the topological structure of the arithmetic sum of two Cantor sets
• On the arithmetic sums of Cantor sets
• Sums of regular Cantor sets, dynamics and applications to number theory
• Stable intersections of regular Cantor sets with large Hausdorff dimensions