Falconer's formula for the Hausdorff dimension of a self-affine set in R2
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Publication:4324894
DOI10.1017/S0143385700008257zbMath0867.28006MaRDI QIDQ4324894
Irene Hueter, Steven P. Lalley
Publication date: 8 July 1997
Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)
Related Items (29)
Dimension of the generalized 4-corner set and its projections ⋮ Hausdorff dimension of planar self-affine sets and measures with overlaps ⋮ An inequality for the matrix pressure function and applications ⋮ Dimension theory of iterated function systems ⋮ Fast approximation of the affinity dimension for dominated affine iterated function systems ⋮ Overlapping self-affine sets of Kakeya type ⋮ Ledrappier-Young formula and exact dimensionality of self-affine measures ⋮ Dimension maximizing measures for self-affine 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 ⋮ The dimensions of inhomogeneous self-affine sets ⋮ Estimating singularity dimension ⋮ On the Ledrappier–Young formula for self-affine measures ⋮ On a generalized dimension of self‐affine fractals ⋮ Domination, almost additivity, and thermodynamic formalism for planar matrix cocycles ⋮ Dimension of the repeller for a piecewise expanding affine map ⋮ Dimensions of an overlapping generalization of Barański carpets ⋮ Non-conformal repellers and the continuity of pressure for matrix cocycles ⋮ Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension ⋮ Planar self-affine sets with equal Hausdorff, box and affinity dimensions ⋮ On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems ⋮ Dimension estimates in smooth dynamics: a survey of recent results ⋮ Dimension and measures on sub-self-affine sets ⋮ AFFINE MAURER–CARTAN INVARIANTS AND THEIR APPLICATIONS IN SELF-AFFINE FRACTALS ⋮ Analyticity of the affinity dimension for planar iterated function systems with matrices which preserve a cone ⋮ A necessary and sufficient condition for a matrix equilibrium state to be mixing ⋮ Equilibrium states of generalised singular value potentials and applications to affine iterated function systems ⋮ Self-affine Sets and the Continuity of Subadditive Pressure
Cites Work
- Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits
- The Hausdorff dimension of general Sierpiński carpets
- The self-affine carpets of McMullen and Bedford have infinite Hausdorff measure
- Products of Random Matrices
- Equilibrium states and the ergodic theory of Anosov diffeomorphisms
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