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An improved convergence case for Diophantine approximations on IFS fractals

Itamar Cohen-Matalon

Vol. 12 (2023), No. 2, 97–115
Abstract

The objective of this paper is to (partially) address the issue of finding an analogue to Khintchine’s theorem for IFS fractals. We study the convergence case for Diophantine approximations and show an improved result for higher dimensions. This matter has been previously studied by Pollington and Velani. They showed a result similar to the one in this paper (a Khintchine convergence case) and we shall show how our result is an improvement in the higher-dimensional cases.

Keywords
IFS, fractals, Diophantine
Mathematical Subject Classification
Primary: 11K60, 37A17
Milestones
Received: 5 March 2022
Revised: 2 May 2023
Accepted: 16 May 2023
Published: 4 June 2023
Authors
Itamar Cohen-Matalon
Department of Mathematics
Tel-Aviv University
Tel-Aviv
Israel