Gibbs measures on self-affine Sierpiński carpets and their singularity spectrum

DOI10.1017/S0143385706001027zbMath1206.82004MaRDI QIDQ5424912

Mounir Mensi, Julien Barral

Publication date: 7 November 2007

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

zbMATH Keywords

multifractal analysisGibbs measuresSierpiński carpetssingularity spectrum

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Fractals (28A80) Ergodic theory (37A99) Dimension theory of smooth dynamical systems (37C45)

Related Items (21)

The packing spectrum for Birkhoff averages on a self-affine repeller ⋮ Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems ⋮ Dimension theory of iterated function systems ⋮ A dimension associated with a cutting of the square of a Gibbs measure ⋮ The multifractal analysis of Birkhoff averages for conformal repellers under random perturbations ⋮ Multifractal analysis for disintegrations of Gibbs measures and conditional Birkhoff averages ⋮ A multifractal formalism for Hewitt-Stromberg measures ⋮ Relations between topological and metrical properties of self-affine Sierpiński sponges ⋮ Distribution of \(\delta \)-connected components of self-affine sponges of Lalley-Gatzouras type ⋮ Random self-affine multifractal Sierpinski sponges in \(\mathbb R^d\) ⋮ Equilibrium states for factor maps between subshifts ⋮ Multifractal formalism for almost all self-affine measures ⋮ Lipschitz classification of Bedford-McMullen carpets with uniform horizontal fibers ⋮ Packing spectra for Bernoulli measures supported on Bedford–McMullen carpets ⋮ Lyapunov spectrum of asymptotically sub-additive potentials ⋮ Variational principle for weighted topological pressure ⋮ Multifractal analysis for Bedford–McMullen carpets ⋮ On the mutual singularity of Hewitt-Stromberg measures ⋮ Inverse Problems in Multifractal Analysis ⋮ Dimension drop of connected part of slicing self-affine sponges ⋮ Additive, almost additive and asymptotically additive potential sequences are equivalent

Cites Work

• Multifractal analysis of infinite products
• Estimates for the lower and the upper dimension of a measure
• Multiperiodic multifractal martingale measures.
• A class of self-affine sets and self-affine measures
• The dimension spectrum of some dynamical systems
• The dimensions of some self-affine limit sets in the plane and hyperbolic sets
• The singularity spectrum for general Sierpiński carpets
• A multifractal formalism
• Large deviation for weak Gibbs measures and multifractal spectra
• The Hausdorff dimension of general Sierpiński carpets
• Generalized dimensions of measures on self-affine sets
• A dimension result arising from the $L^q$-spectrum of a measure
• Fractal Dimensions and Random Transformations
• The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples
• On the multifractal analysis of measures

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