Quantitative recurrence properties for self-conformal sets

DOI10.1090/proc/15285zbMath1458.28002arXiv1909.08913OpenAlexW3107047164MaRDI QIDQ5150186

No author found.

Publication date: 10 February 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.08913

zbMATH Keywords

Hausdorff measureself-conformal setsquantitative recurrence

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80)

Related Items

Dynamically defined subsets of generic self-affine sets* ⋮ A strong Borel–Cantelli lemma for recurrence ⋮ Dynamical Borel–Cantelli lemma for recurrence theory ⋮ ON THE HAUSDORFF MEASURE OF SHRINKING TARGET SETS ON SELF‐CONFORMAL SETS ⋮ On Shrinking Targets and Self-returning Points ⋮ Hausdorff dimensions of recurrent and shrinking target sets under Lipschitz functions for expanding Markov maps ⋮ Stochastics and dynamics of fractals ⋮ Quantitative recurrence and the shrinking target problem for overlapping iterated function systems ⋮ Modified shrinking target problems on self-conformal sets ⋮ Dynamical Borel–Cantelli lemma for recurrence under Lipschitz twists

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantitative recurrence properties for beta-dynamical system
• Quantitative mixing results and inner functions
• Quantitative recurrence results
• The ergodic theory of shrinking targets
• Quantitative recurrence properties in conformal iterated function systems
• Measure theoretic laws for lim sup sets
• A Survey on the Dimension Theory in Dynamical Diophantine Approximation
• Quantitative recurrence properties and homogeneous self-similar sets
• On natural invariant measures on generalised iterated function systems
• Repellers for real analytic maps
• Self‐conformal sets with positive Hausdorff measure
• An analogue of Khintchine's theorem for self-conformal sets
• The shrinking target problem in the dynamical system of continued fractions
• Dynamical Borel-Cantelli lemmas for Gibbs measures
• Hausdorff dimension of measures via Poincaré recurrence