IFS分形上Diophantine近似的改进收敛情形

Q4 Mathematics

Moscow Journal of Combinatorics and Number Theory Pub Date : 2022-01-23 DOI:10.2140/moscow.2023.12.97

Itamar Cohen-Matalon

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引用次数: 0

摘要

本文的目的是（部分）解决寻找IFS分形的Khintchine定理的类似物的问题。我们研究了丢番图近似的收敛情况，并给出了高维的改进结果。Pollington和Velani之前在arXiv:math/0401149中对此事进行了研究。Pollington和Velani给出了与本文相似的结果（Khinchine收敛情况），我们将展示我们的结果如何在高维情况下得到改进。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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An improved convergence case for Diophantine approximations on IFS fractals

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 in arXiv:math/0401149. Pollington and Velani show a similar result to the one in this paper (a Khinchine convergence case) and we shall show how our result is an improvement in the higher dimensional cases.

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来源期刊

Moscow Journal of Combinatorics and Number Theory Mathematics-Algebra and Number Theory

CiteScore

0.80

自引率

0.00%

发文量