Non-\(L^1\) functions with rotation sets of Hausdorff dimension one

DOI10.1007/s10474-009-8204-0zbMath1224.37002OpenAlexW2055409901MaRDI QIDQ624217

Zoltán Buczolich

Publication date: 8 February 2011

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-009-8204-0

zbMATH Keywords

rotationHausdorff dimensioncontinued fractionergodic average

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Dynamical systems involving maps of the circle (37E10) Ergodic theorems, spectral theory, Markov operators (37A30) Hausdorff and packing measures (28A78)

Related Items (2)

Convergence of ergodic averages for many group rotations ⋮ Good and Bad Functions for Bad Processes

Cites Work

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• Computing the dimension of dynamically defined sets: E_2 and bounded continued fractions
• HAUSDORFF DIMENSION OF SETS OF CONTINUED FRACTIONS
• Conformal iterated function systems with applications to the geometry of continued fractions
• Measure and dimension functions: measurability and densities
• Arithmetic averages of rotations of measurable functions
• Renewal-type limit theorem for the Gauss map and continued fractions
• A function with locally uncountable rotation set

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