Dimension of invariant measures for maps with exponent zero

DOI10.1017/S0143385700003187zbMath0608.28008OpenAlexW2158795258MaRDI QIDQ3748515

Michał Misiurewicz, François Ledrappier

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1017/s0143385700003187

zbMATH Keywords

entropyHausdorff dimensionLyapunov exponentdimension of invariant measuresnon-atomic ergodic probability measurestable manifold of Feigenbaum's fixed point

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Ergodic theory (37A99)

Related Items (18)

Absolutely continuous invariant measures for \(C^ 2\) unimodal maps satisfying the Collet-Eckmann conditions ⋮ Dimension of Gibbs measures with infinite entropy ⋮ Lifting measures to Markov extensions ⋮ Generalized dimensions, entropies, and Lyapunov exponents from the pressure function for strange sets. ⋮ Some results on the behavior and estimation of the fractal dimensions of distributions on attractors ⋮ Dimension, recurrence via entropy and Lyapunov exponents for map with singularities ⋮ On the dimension of deterministic and random Cantor-like sets, symbolic dynamics, and the Eckmann-Ruelle conjecture ⋮ Possible jumps of entropy for interval maps ⋮ The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples ⋮ Dimension theory for invariant measures of endomorphisms ⋮ Measure of solenoidal attractors of unimodal maps of the segment ⋮ On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions ⋮ Dimensional characteristics of invariant measures for circle diffeomorphisms ⋮ A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions ⋮ Pointwise dimension, entropy and Lyapunov exponents for $C^{1}$ maps ⋮ Unnamed Item ⋮ Dynamics and universality of unimodal mappings with infinite criticality ⋮ On Hausdorff dimension of some Cantor attractors

Cites Work

• Universal properties of maps on an interval
• On the existence of Feigenbaum's fixed point
• Structure of mappings of an interval with zero entropy
• Some relations between dimension and Lyapunov exponents
• An inequality for the entropy of differentiable maps
• A computer-assisted proof of the Feigenbaum conjectures
• Unnamed Item

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