Intrinsic Diophantine approximation for overlapping iterated function systems
CC BY
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| Định dạng: | Sách |
| Ngôn ngữ: | English |
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s00208-023-02608-8 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7545 |
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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 |
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8.8926115 |