Almost additive multifractal analysis

DOI10.1016/J.MATPUR.2009.04.006zbMath1186.37033OpenAlexW1980321098MaRDI QIDQ923872

Paulo Doutor, Luis Barreira

Publication date: 24 July 2009

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2009.04.006

zbMATH Keywords

variational principlemultifractal analysishyperbolic flow

Mathematics Subject Classification ID

Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dimension theory of smooth dynamical systems (37C45)

Related Items (27)

On the mixed multifractal formalism for vector-valued measures ⋮ The spectral properties of the strongly coupled Sturm Hamiltonian of eventually constant type ⋮ Multifractal analysis of dimension spectrum in non-uniformly hyperbolic systems ⋮ The thermodynamic approach to multifractal analysis ⋮ Dimension estimates for arbitrary subsets of limit sets of a Markov construction and related multifractal analysis ⋮ Almost additive topological pressure of proper systems ⋮ Constrained ergodic optimization for asymptotically additive potentials ⋮ On the topological entropy of saturated sets for amenable group actions ⋮ \(q\)-pressure for dynamical systems ⋮ A generalization of O’Neil’s theorems for projections of measures and dimensions ⋮ HAUSDORFF DIMENSION OF THE IRREGULAR SET IN NON-UNIFORMLY HYPERBOLIC SYSTEMS ⋮ Domination, almost additivity, and thermodynamic formalism for planar matrix cocycles ⋮ Multifractal analysis of asymptotically additive sequences ⋮ Transitively-saturated property, Banach recurrence and Lyapunov regularity ⋮ Distributional chaos in multifractal analysis, recurrence and transitivity ⋮ Q-entropy for general topological dynamical systems ⋮ Zero temperature limits of Gibbs states for almost-additive potentials ⋮ Intermediate Lyapunov exponents for systems with periodic orbit gluing property ⋮ The asymptotically additive topological pressure on the irregular set for asymptotically additive potentials ⋮ ALMOST ADDITIVE THERMODYNAMIC FORMALISM: SOME RECENT DEVELOPMENTS ⋮ Topological pressure dimension for almost additive potentials ⋮ Additive, almost additive and asymptotically additive potential sequences are equivalent ⋮ Almost additive multifractal analysis for flows ^* ⋮ THE STABILITY OF HAUSDORFF DIMENSION FOR THE LEVEL SETS UNDER THE PERTURBATION OF CONFORMAL REPELLERS ⋮ On the Projections of the Mutual Multifractal Renyi Dimensions ⋮ Unstable entropies and dimension theory of partially hyperbolic systems ⋮ Dimension spectra for flows: future and past

Cites Work

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• Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures
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• Dimension and recurrence in hyperbolic dynamics
• Higher-dimensional multifractal analysis
• The dimension spectrum of some dynamical systems
• Sets of ``non-typical points have full topological entropy and full Hausdorff dimension
• Fractal measures and their singularities: The characterization of strange sets
• The singularity spectrumf(α) for cookie-cutters
• A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems
• The Dimension Spectrum of the Maximal Measure
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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