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Intrinsic Diophantine approximation for overlapping iterated function systems

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Bibliographic Details
Main Author: Simon, Baker
Format: Book
Language:English
Published: Springer 2023
Subjects:
analogue of Khintchine’s theorem
Online Access:https://link.springer.com/article/10.1007/s00208-023-02608-8
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7545
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spelling oai:localhost:PNK-75452023-04-05T03:48:45Z Intrinsic Diophantine approximation for overlapping iterated function systems Simon, Baker analogue of Khintchine’s theorem CC BY In this paper we study a family of limsup sets that are defined using iterated function systems. Our main result is an analogue of Khintchine’s theorem for these sets. We then apply this result to the topic of intrinsic Diophantine Approximation on self-similar sets. In particular, we define a new height function for an element of Qd contained in a self-similar set in terms of its eventually periodic representations. For limsup sets defined with respect to this height function, we obtain a detailed description of their metric properties. The results of this paper hold in arbitrary dimensions and without any separation conditions on the underlying iterated function system. 2023-04-05T03:48:45Z 2023-04-05T03:48:45Z 2023 Book https://link.springer.com/article/10.1007/s00208-023-02608-8 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7545 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic analogue of Khintchine’s theorem
spellingShingle analogue of Khintchine’s theorem
Simon, Baker
Intrinsic Diophantine approximation for overlapping iterated function systems
description CC BY
format Book
author Simon, Baker
author_facet Simon, Baker
author_sort Simon, Baker
title Intrinsic Diophantine approximation for overlapping iterated function systems
title_short Intrinsic Diophantine approximation for overlapping iterated function systems
title_full Intrinsic Diophantine approximation for overlapping iterated function systems
title_fullStr Intrinsic Diophantine approximation for overlapping iterated function systems
title_full_unstemmed Intrinsic Diophantine approximation for overlapping iterated function systems
title_sort intrinsic diophantine approximation for overlapping iterated function systems
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s00208-023-02608-8
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7545
_version_ 1762365500703113216
score 8.891145

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