Intrinsic Diophantine approximation for overlapping iterated function systems

DOI10.1007/s00208-023-02608-8arXiv2104.14249OpenAlexW3158308821MaRDI QIDQ6117878

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Publication date: 21 February 2024

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.14249

zbMATH Keywords

Diophantine approximation iterated function system Hausdorff measure self-similar set Khintchine's theorem mass transference principle

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80) Metric theory (11J83)

Cites Work

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Metric Diophantine approximation on the middle-third Cantor set
Intrinsic approximation on Cantor-like sets, a problem of Mahler
On self-similar sets with overlaps and inverse theorems for entropy
On a problem of K. Mahler: Diophantine approximation and Cantor sets
Badly approximable points on manifolds
Diophantine approximation and Cantor sets
Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals
On fractal measures and Diophantine approximation
The ergodic theory of shrinking targets
Extrinsic Diophantine approximation on manifolds and fractals
Random walks on homogeneous spaces and Diophantine approximation on fractals
A mass transference principle and the Duffin-Schaeffer conjecture for Hausdorff measures
Random walks, spectral gaps, and Khintchine's theorem on fractals
Almost no points on a Cantor set are very well approximable
Intrinsic approximation for fractals defined by rational iterated function systems: Mahler's research suggestion
Approximation properties of -expansions II
Measure theoretic laws for lim sup sets
Some suggestions for further research
Intrinsic Diophantine approximation on manifolds: General theory
Diophantine Approximation on Manifolds and the Distribution of Rational Points: Contributions to the Convergence Theory
ON THE DIOPHANTINE PROPERTIES OF λ ‐EXPANSIONS
Analogues of Khintchine’s theorem for random attractors
Proof of the exact overlaps conjecture for systems with algebraic contractions
On intrinsic and extrinsic rational approximation to Cantor sets
An analogue of Khintchine's theorem for self-conformal sets
Approximation properties of β-expansions
A Frostman-Type Lemma for Sets with Large Intersections, and an Application to Diophantine Approximation
Probability Inequalities for Sums of Bounded Random Variables
A note on the Borel-Cantelli lemma
ON THE HAUSDORFF MEASURE OF SHRINKING TARGET SETS ON SELF‐CONFORMAL SETS
Overlapping Iterated Function Systems from the Perspective of Metric Number Theory

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