Multifractal spectrum of quotients of Birkhoff averages for a family of quadratic maps

DOI10.1080/1726037X.2017.1413064zbMath1499.37057OpenAlexW2808684533MaRDI QIDQ5029582

Fernando Vericat, Alejandro M. Mesón

Publication date: 14 February 2022

Published in: Journal of Dynamical Systems and Geometric Theories (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/1726037x.2017.1413064

zbMATH Keywords

multifractal spectrumBenedicks-Carleson mapsquotients of Birkhoff averages

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Fractals (28A80) Topological entropy (37B40) Dimension theory of smooth dynamical systems (37C45)

Cites Work

• Large deviation principle for Benedicks-Carleson quadratic maps
• The dynamics of the Hénon map
• On iterations of \(1-\alpha x^2\) on \((-1,1)\)
• A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions
• The Lyapunov spectrum for conformal expanding maps and Axiom-A surface diffeomorphisms
• Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages.
• Sets of ``non-typical points have full topological entropy and full Hausdorff dimension
• Multifractal formalism for Benedicks–Carleson quadratic maps
• Bowen’s equation in the non-uniform setting
• Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps
• Multifractal Analysis for Quotients of Birkhoff Sums for Countable Markov Maps

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