On self-similar measures with absolutely continuous projections and dimension conservation in each direction

DOI10.1017/etds.2019.39zbMath1454.28013arXiv1809.09923OpenAlexW2962744481WikidataQ127616806 ScholiaQ127616806MaRDI QIDQ5131224

Ariel Rapaport

Publication date: 4 November 2020

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.09923

zbMATH Keywords

absolute continuityself-similar sets and measuresdimension conservation

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Hausdorff and packing measures of slices of dynamically defined sets
• Local entropy averages and projections of fractal measures
• Relationships between different dimensions of a measure
• A self-similar measure with dense rotations, singular projections and discrete slices
• On Furstenberg's intersection conjecture, self-similar measures, and the \(L^q\) norms of convolutions
• On the exceptional set for absolute continuity of Bernoulli convolutions
• Absolute continuity of self-similar measures, their projections and convolutions
• Exact dimensionality and projections of random self-similar measures and sets
• Dimension theory of iterated function systems
• Dimension Conservation for Self-Similar Sets and Fractal Percolation
• Resonance between Cantor sets
• How projections affect the dimension spectrum of fractal measures
• Hausdorff and packing dimensions and sections of measures
• The equivalence of some Bernoulli convolutions to Lebesgue measure
• Absolute continuity of complex Bernoulli convolutions
• Ergodic fractal measures and dimension conservation
• Ergodic Theory