On the 𝐿^{𝑞}-spectrum of planar self-affine measures

DOI10.1090/TRAN/6523zbMath1342.28014arXiv1310.1789OpenAlexW1948100134MaRDI QIDQ2790706

Jonathan M. Fraser

Publication date: 8 March 2016

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

Full work available at URL: https://arxiv.org/abs/1310.1789

zbMATH Keywords

Hausdorff dimensionself-affine measure\(L^q\) spectrummodified singular value function

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Eigenvalues, singular values, and eigenvectors (15A18) Fractals (28A80) Hausdorff and packing measures (28A78) Dimension theory of smooth dynamical systems (37C45)

Related Items (7)

On the $L^q$-dimensions of measures on Hueter-Lalley type self-affine sets ⋮ An explicit formula for the pressure of box-like affine iterated function systems ⋮ The Lq$L^q$ spectrum of self‐affine measures on sponges ⋮ Box-counting dimension and differentiability of box-like statistically self-affine functions ⋮ -spectra of measures on planar non-conformal attractors ⋮ The box-counting dimension of random box-like 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
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Random self-affine multifractal Sierpinski sponges in \(\mathbb R^d\)
• Hausdorff dimension of the limit sets of some planar geometric constructions
• Self-affine multifractal Sierpiński sponges in \(\mathbb{R}^d\)
• Relationships between different dimensions of a measure
• A class of self-affine sets and self-affine measures
• An improved multifractal formalism and self-similar measures
• The singularity spectrum for general Sierpiński carpets
• A multifractal formalism
• Hausdorff dimensions of sofic affine-invariant sets
• Multifractal formalism for almost all self-affine measures
• Existence of L^q dimensions and entropy dimension for self-conformal measures
• On the packing dimension of box-like self-affine sets in the plane
• Multifractal spectra of random self-affine multifractal Sierpinski sponges in $\mathbb{R}^d$
• The Hausdorff dimension of the projections of self-affine carpets
• Multifractal analysis for Bedford–McMullen carpets
• The packing spectrum for Birkhoff averages on a self-affine repeller
• The Hausdorff dimension of general Sierpiński carpets
• Hausdorff Dimension in Graph Directed Constructions
• DIMENSIONS OF SELF-AFFINE FRACTALS AND MULTIFRACTALS GENERATED BY UPPER-TRIANGULAR MATRICES
• Generalized dimensions of measures on almost self-affine sets
• TheL^q-spectrum of a class of graph directed self-affine measures
• Dimension, entropy and Lyapunov exponents
• The Hausdorff dimension of self-affine fractals
• Generalized dimensions of measures on self-affine sets
• A dimension result arising from the $L^q$-spectrum of a measure
• SMOOTHNESS OF THE $L^{\lowercase{q}}$-SPECTRUM OF SELF-SIMILAR MEASURES WITH OVERLAPS
• Measures of full dimension on affine-invariant sets
• Multifractal analysis on the flexed Sierpiński gasket

This page was built for publication: On the 𝐿^{𝑞}-spectrum of planar self-affine measures