Local dimension for piecewise monotonic maps on the interval

DOI10.1017/S0143385700009822zbMath0842.58019OpenAlexW2160720146MaRDI QIDQ4863813

Franz Hofbauer

Publication date: 4 August 1996

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

Full work available at URL: https://doi.org/10.1017/s0143385700009822

zbMATH Keywords

intervalHausdorff dimensionmultifractal formalismergodic invariant measurepiecewise monotonic maps

Mathematics Subject Classification ID

Ergodic theory (37A99) Low-dimensional dynamical systems (37E99) Hausdorff and packing measures (28A78)

Related Items (17)

Extremality and dynamically defined measures. I: Diophantine properties of quasi-decaying measures ⋮ Multifractal formalism for Benedicks–Carleson quadratic maps ⋮ The box dimension of completely invariant subsets for expanding piecewise monotonic transformations ⋮ The thermodynamic approach to multifractal analysis ⋮ Unnamed Item ⋮ Perturbations of set-valued dynamical systems, with applications to game theory ⋮ Non-algebraic convergence proofs for continuous-time fictitious play ⋮ Equilibrium states, pressure and escape for multimodal maps with holes ⋮ Dimension of the repeller for a piecewise expanding affine map ⋮ On shrinking targets for piecewise expanding interval maps ⋮ Birkhoff spectrum for piecewise monotone interval maps ⋮ Thermodynamic formalism for interval maps: inducing schemes ⋮ Dimension theory for multimodal maps ⋮ BIRKHOFF SPECTRA FOR ONE-DIMENSIONAL MAPS WITH SOME HYPERBOLICITY ⋮ Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches ⋮ Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems ⋮ Shrinking targets in parametrised families

Cites Work

• Unnamed Item
• Piecewise invertible dynamical systems
• Generic properties of invariant measures for continuous piecewise monotonic transformations
• Ergodic theory on compact spaces
• Connecting ergodicity and dimension in dynamical systems
• Fractal measures and their singularities: The characterization of strange sets
• Matrix Analysis
• The singularity spectrumf(α) for cookie-cutters
• Equilibrium states for piecewise monotonic transformations
• Fractal Properties of Invariant Subsets for Piecewise Monotonic Maps on the Interval

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