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Abstract
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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.
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Keywords
IFS, fractals, Diophantine
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Mathematical Subject Classification
Primary: 11K60, 37A17
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Milestones
Received: 5 March 2022
Revised: 2 May 2023
Accepted: 16 May 2023
Published: 4 June 2023
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| © 2023 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers). |
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