On self-affine measures with equal Hausdorff and Lyapunov dimensions

DOI10.1090/tran/7099zbMath1386.37021arXiv1511.06893OpenAlexW2963949992MaRDI QIDQ4635478

Ariel Rapaport

Publication date: 23 April 2018

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

Full work available at URL: https://arxiv.org/abs/1511.06893

zbMATH Keywords

random matrixself-affine measureFurstenberg measure

Mathematics Subject Classification ID

Fractals (28A80) Dimension theory of smooth dynamical systems (37C45)

Related Items (14)

Hausdorff dimension of planar self-affine sets and measures with overlaps ⋮ Ledrappier-Young formula and exact dimensionality of self-affine measures ⋮ Dimension maximizing measures for self-affine systems ⋮ Dimension of invariant measures for affine iterated function systems ⋮ On the $L^q$-dimensions of measures on Hueter-Lalley type self-affine sets ⋮ Hausdorff dimension of planar self-affine sets and measures ⋮ A converse statement to Hutchinson's theorem and a dimension gap for self-affine measures ⋮ On the dimension of Furstenberg measure for \({SL}_{2}(\mathbb {R})\) random matrix products ⋮ An explicit formula for the pressure of box-like affine iterated function systems ⋮ The Lq$L^q$ spectrum of self‐affine measures on sponges ⋮ Dimension of the repeller for a piecewise expanding affine map ⋮ On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems ⋮ On the dimension of triangular self-affine sets ⋮ Equilibrium states of generalised singular value potentials and applications to affine iterated function systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Furstenberg measure and density of states for the Anderson-Bernoulli model at small disorder
• Hausdorff dimension for randomly perturbed self affine attractors
• A reduction technique for limit theorems in analysis and probability theory
• On the dimension of Furstenberg measure for \({SL}_{2}(\mathbb {R})\) random matrix products
• Random Walks on Reductive Groups
• Dimension theory of iterated function systems
• The Hausdorff dimension of general Sierpiński carpets
• The Hausdorff dimension of self-affine fractals
• Hausdorff and packing dimensions and sections of measures
• Measure and dimension for some fractal families
• Planar self-affine sets with equal Hausdorff, box and affinity dimensions
• Finitely Supported Measures on $$S{L}_{2}(\mathbb{R})$$ Which are Absolutely Continuous at Infinity
• Dimensions of Self-affine Sets: A Survey
• Fourier Analysis and Hausdorff Dimension
• On the Ledrappier–Young formula for self-affine measures

This page was built for publication: On self-affine measures with equal Hausdorff and Lyapunov dimensions