Intrinsic approximation for fractals defined by rational iterated function systems: Mahler's research suggestion

DOI10.1112/plms/pdu002zbMath1309.11059arXiv1208.2089OpenAlexW3103450921MaRDI QIDQ2874668

David Simmons, Lior Fishman

Publication date: 8 August 2014

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

Full work available at URL: https://arxiv.org/abs/1208.2089

zbMATH Keywords

diophantine approximationfractalintrinsic approximation

Mathematics Subject Classification ID

Metric theory (11J83) Hausdorff and packing measures (28A78) Homogeneous approximation to one number (11J04)

Related Items (15)

The distribution of rational numbers on Cantor's middle thirds set ⋮ Metric Diophantine approximation on the middle-third Cantor set ⋮ Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals ⋮ Intrinsic Diophantine approximation on manifolds: General theory ⋮ Diophantine approximation in metric space ⋮ Intrinsic Diophantine approximation for overlapping iterated function systems ⋮ Mahler's question for intrinsic Diophantine approximation on triadic Cantor set: the divergence theory ⋮ APPROXIMATING NUMBERS OF THE CANTOR SET BY ALGEBRAIC NUMBERS ⋮ Badly approximable points on self-affine sponges and the lower Assouad dimension ⋮ On intrinsic and extrinsic rational approximation to Cantor sets ⋮ A Mahler miscellany ⋮ An analogue of Khintchine's theorem for self-conformal sets ⋮ Diophantine approximation in Banach spaces ⋮ Extrinsic Diophantine approximation on manifolds and fractals ⋮ Dyadic approximation in the middle-third Cantor set

Cites Work

• Unnamed Item
• Unnamed Item
• Intrinsic approximation on Cantor-like sets, a problem of Mahler
• Badly approximable vectors on fractals
• Schmidt's game on fractals
• On a problem of K. Mahler: Diophantine approximation and Cantor sets
• Diophantine approximation and Cantor sets
• On fractal measures and Diophantine approximation
• Diophantine approximation and badly approximable sets
• Almost no points on a Cantor set are very well approximable
• Some suggestions for further research

This page was built for publication: Intrinsic approximation for fractals defined by rational iterated function systems: Mahler's research suggestion