Multifractal analysis of non-uniformly hyperbolic systems

DOI10.1007/s11856-010-0040-yzbMath1214.37029arXiv0801.1383OpenAlexW2594203795MaRDI QIDQ611024

Anders Öberg, Mark Pollicott, Thomas M. Jordan, Anders Johansson

Publication date: 13 December 2010

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.1383

zbMATH Keywords

Hausdorff dimensionmultifractal analysisBirkhoff averagenon-uniformly hyperbolicManneville-Pomeau map

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Fractals (28A80) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dimension theory of smooth dynamical systems (37C45)

Related Items (21)

The packing spectrum for Birkhoff averages on a self-affine repeller ⋮ Birkhoff spectrum for Hénon-like maps at the first bifurcation ⋮ Multifractal analysis of dimension spectrum in non-uniformly hyperbolic systems ⋮ The thermodynamic approach to multifractal analysis ⋮ Mingled hyperbolicities: ergodic properties and bifurcation phenomena (an approach using concavity) ⋮ Higher dimensional multifractal analysis of non-uniformly hyperbolic systems ⋮ HAUSDORFF DIMENSION OF THE IRREGULAR SET IN NON-UNIFORMLY HYPERBOLIC SYSTEMS ⋮ Infinite non-conformal iterated function systems ⋮ Multifractal analysis of ergodic averages in some non-uniformly hyperbolic systems ⋮ Generic Birkhoff spectra ⋮ Multifractal analysis of Birkhoff averages for typical infinitely generated self-affine sets ⋮ Multifractal analysis of weighted ergodic averages ⋮ Entropy-approachability for transitive Markov shifts over infinite alphabet ⋮ Birkhoff spectrum for piecewise monotone interval maps ⋮ Lyapunov spectrum for Hénon-like maps at the first bifurcation ⋮ Transience and multifractal analysis ⋮ Multifractal analysis of the historic set in non-uniformly hyperbolic systems ⋮ Multifractal analysis of Birkhoff averages for countable Markov maps ⋮ Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches ⋮ Multifractal analysis of geodesic flows on surfaces without focal points ⋮ Multifractal analysis in non-uniformly hyperbolic interval maps

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• A multifractal formalism for growth rates and applications to geometrically finite Kleinian groups
• Multifractal formalism for some parabolic maps
• The Lyapunov spectrum of some parabolic systems

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