The sets of divergence points of self-similar measures are residual

DOI10.1016/j.jmaa.2013.03.043zbMath1304.28008OpenAlexW2084864403MaRDI QIDQ488676

Yong-Cai Geng, Sumit K. Garg

Publication date: 26 January 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2013.03.043

zbMATH Keywords

residualopen set conditiondivergence pointself-similar measure

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Fractals (28A80)

Related Items

On the exceptional sets concerning the leading partial quotient in continued fractions, Generic property of irregular sets in systems satisfying the specification property, A note on exceptional sets in Erdős-Rényi limit theorem, Lyapunov irregular set of Banach cocycles, LOCAL GEOMETRY OF SELF-SIMILAR SETS: TYPICAL BALLS, TANGENT MEASURES AND ASYMPTOTIC SPECTRA, SOME TOPOLOGICAL RESULTS ON LEVEL SETS AND MULTIFRACTAL SETS, On exceptional sets in Erdős-Rényi limit theorem, Ergodic properties of systems with asymptotic average shadowing property, Topological pressure for the completely irregular set of Birkhoff averages, On exceptional sets in Erdős-Rényi limit theorem revisited, A note on the rate of returns in random walks, Points with maximal Birkhoff average oscillation, The asymptotically additive topological pressure: variational principle for non-compact and intersection of irregular sets, Quantitative recurrence properties in the historic set for symbolic systems, A note on the distribution of the digits in Cantor expansions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Divergence points of self-similar measures satisfying the OSC
• Ergodic limits on the conformal repellers
• Multifractal formalism for self-similar measures with weak separation condition
• Baire category and extremely non-normal points of invariant sets of IFS's
• Topological pressure and the variational principle for noncompact sets
• Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages.
• The pointwise dimension of self-similar measures
• On Bandt's tangential distribution for self-similar measures
• On absolutely continuous invariant measures with respect to Hausdorff measures on self-similar sets
• Divergence points in systems satisfying the specification property
• Sets of ``non-typical points have full topological entropy and full Hausdorff dimension
• Irregular sets are residual
• Topological and fractal properties of real numbers which are not normal
• Iterated Cesàro averages, frequencies of digits, and Baire category
• Hausdorff dimensions of the divergence points of self-similar measures with the open set condition
• RECURRENCE, DIMENSION AND ENTROPY
• The irregular set for maps with the specification property has full topological pressure
• NORMAL AND NON-NORMAL POINTS OF SELF-SIMILAR SETS AND DIVERGENCE POINTS OF SELF-SIMILAR MEASURES
• Extremely non-normal numbers