Measure and dimension for some fractal families
From MaRDI portal
Publication:4224169
DOI10.1017/S0305004198002680zbMath0927.28006OpenAlexW2128554376MaRDI QIDQ4224169
Publication date: 27 April 1999
Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0305004198002680
Hausdorff dimensionself-similar setsHausdorff measuresTakagi functionself-affine setsWeierstraß functions
Related Items (90)
Moments of infinite convolutions of symmetric Bernoulli distributions ⋮ Dimensions of a class of self-affine Moran sets ⋮ Dynamically defined subsets of generic self-affine sets* ⋮ On dense intermingling of exact overlaps and the open set condition ⋮ Hausdorff dimension of planar self-affine sets and measures with overlaps ⋮ On affine iterated function systems which robustly admit an invariant affine subspace ⋮ Dimension estimates for iterated function systems and repellers. Part II ⋮ Finite-dimensional behaviour and observability in a randomly forced PDE ⋮ An inequality for the matrix pressure function and applications ⋮ Dimension theory of iterated function systems ⋮ Overlapping self-affine sets of Kakeya type ⋮ Hausdorff dimension of the limit sets of some planar geometric constructions ⋮ Ledrappier-Young formula and exact dimensionality of self-affine measures ⋮ Pointwise regularity of parameterized affine zipper fractal curves ⋮ Dimensions of random statistically self-affine Sierpinski sponges in \(\mathbb{R}^k\) ⋮ Gap sequences and Topological properties of Bedford–McMullen sets* ⋮ Hausdorff dimension for randomly perturbed self affine attractors ⋮ Connectedness locus for pairs of affine maps and zeros of power series ⋮ Dimension maximizing measures for self-affine systems ⋮ Quasi-multiplicativity of typical cocycles ⋮ DIMENSIONS OF SELF-AFFINE FRACTALS AND MULTIFRACTALS GENERATED BY UPPER-TRIANGULAR MATRICES ⋮ Transversal families of nonlinear projections and generalizations of Favard length ⋮ Dimension of invariant measures for affine iterated function systems ⋮ Dimension and measure of sums of planar sets and curves ⋮ Hausdorff dimension of planar self-affine sets and measures ⋮ A converse statement to Hutchinson's theorem and a dimension gap for self-affine measures ⋮ Dimensions of projected sets and measures on typical self-affine sets ⋮ On the dimension of the graph of the classical Weierstrass function ⋮ Hausdorff and box dimensions of self-affine sets in a locally compact non-Archimedean field ⋮ Overlapping Iterated Function Systems from the Perspective of Metric Number Theory ⋮ Gap sequences of McMullen sets ⋮ Box-counting dimension and differentiability of box-like statistically self-affine functions ⋮ DOUBLING PROPERTIES OF SELF-AFFINE MEASURES SUPPORTED ON GATZOURAS–LALLEY FRACTALS ⋮ Multifractal formalism for almost all self-affine measures ⋮ Estimating singularity dimension ⋮ On the Ledrappier–Young formula for self-affine measures ⋮ Random affine code tree fractals: Hausdorff and affinity dimensions and pressure ⋮ Invariant measures in non-conformal fibered systems with singularities ⋮ Quantitative recurrence and the shrinking target problem for overlapping iterated function systems ⋮ On a generalized dimension of self‐affine fractals ⋮ Entropy production for a class of inverse SRB measures ⋮ Dimension of the repeller for a piecewise expanding affine map ⋮ On the dimensions of a family of overlapping self-affine carpets ⋮ Dimensions of an overlapping generalization of Barański carpets ⋮ Multifractal analysis of Birkhoff averages for typical infinitely generated self-affine sets ⋮ Measure-theoretic degrees and topological pressure for non-expanding transformations ⋮ Exceptional sets for self-affine fractals ⋮ On the Fibonacci-Mandelbrot set ⋮ Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions ⋮ A topological separation condition for fractal attractors ⋮ Non-conformal repellers and the continuity of pressure for matrix cocycles ⋮ ON THE DIMENSION OF SELF-SIMILAR SETS ⋮ On self-affine measures with equal Hausdorff and Lyapunov dimensions ⋮ Dimension of generic self-affine sets with holes ⋮ 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 ⋮ Invariant measures for parabolic IFS with overlaps and random continued fractions ⋮ Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups ⋮ Dimensions of random affine code tree fractals ⋮ Exceptional sets for self-similar fractals in Carnot groups ⋮ “Mandelbrot set” for a pair of linear maps: The local geometry ⋮ Number theoretical peculiarities in the dimension theory of dynamical systems. ⋮ A GENERAL RESULT ON ABSOLUTE CONTINUITY OF NON-UNIFORM SELF-SIMILAR MEASURES ON THE REAL LINE ⋮ The box dimensions of exceptional self-affine sets in \(\mathbb{R}^3\) ⋮ AFFINE MAURER–CARTAN INVARIANTS AND THEIR APPLICATIONS IN SELF-AFFINE FRACTALS ⋮ Dimension of fractional Brownian motion with variable drift ⋮ The box-counting dimension of random box-like self-affine sets ⋮ Dimension of the Graphs of the Weierstrass-Type Functions ⋮ On the dimension of triangular self-affine sets ⋮ Bernoulli convolutions and an intermediate value theorem for entropies of \(k\)-partitions ⋮ On the dimension of self-affine sets and measures with overlaps ⋮ Recurrence to Shrinking Targets on Typical Self-Affine Fractals ⋮ Random affine code tree fractals and Falconer–Sloan condition ⋮ Triangular Gatzouras–Lalley-type planar carpets with overlaps ⋮ Dimension theory of some non-Markovian repellers. I: A gentle introduction ⋮ Dimension theory of some non-Markovian repellers. II: Dynamically defined function graphs ⋮ Self-similar sets of zero Hausdorff measure and positive packing measure ⋮ RANDOM SUBSETS OF SELF‐AFFINE FRACTALS ⋮ Multiparameter Projection Theorems with Applications to Sums-Products and Finite Point Configurations in the Euclidean Setting ⋮ Equilibrium states of generalised singular value potentials and applications to affine iterated function systems ⋮ Self-similar measures and intersections of Cantor sets ⋮ The Hausdorff dimension of some planar sets with unbounded digits ⋮ Dimension estimates for non-conformal repellers and continuity of sub-additive topological pressure ⋮ Local dimensions of measures on infinitely generated self-affine sets ⋮ Remarks on the analyticity of subadditive pressure for products of triangular matrices ⋮ Self-affine Sets and the Continuity of Subadditive Pressure ⋮ Continuity of sub-additive topological pressure with matrix cocycles * ⋮ Absolutely continuous convolutions of singular measures and an application to the square Fibonacci Hamiltonian ⋮ Typical absolute continuity for classes of dynamically defined measures
This page was built for publication: Measure and dimension for some fractal families
