On a class of self-similar sets which contain finitely many common points

Kan Jiang; Derong Kong; Wenxia Li; Zhiqiang Wang

doi:10.1017/prm.2024.66

On a class of self-similar sets which contain finitely many common points

Kan Jiang
, Derong Kong
, Wenxia Li
, Zhiqiang Wang^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

For let be a self-similar set generated by the iterated function system. Given, let be the set of such that. In this paper we show that is a topological Cantor set having zero Lebesgue measure and full Hausdorff dimension. Furthermore, we show that for any there exists a full Hausdorff dimensional set of such that.

Original language	English
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
DOIs	https://doi.org/10.1017/prm.2024.66
State	Accepted/In press - 2024

Keywords

Cantor set
Hausdorff dimension
intersection
self-similar set
thickness

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10.1017/prm.2024.66

Cite this

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title = "On a class of self-similar sets which contain finitely many common points",

abstract = "For let be a self-similar set generated by the iterated function system. Given, let be the set of such that. In this paper we show that is a topological Cantor set having zero Lebesgue measure and full Hausdorff dimension. Furthermore, we show that for any there exists a full Hausdorff dimensional set of such that.",

keywords = "Cantor set, Hausdorff dimension, intersection, self-similar set, thickness",

author = "Kan Jiang and Derong Kong and Wenxia Li and Zhiqiang Wang",

note = "Publisher Copyright: Copyright {\textcopyright} The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.",

year = "2024",

doi = "10.1017/prm.2024.66",

language = "英语",

journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",

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AU - Jiang, Kan

AU - Kong, Derong

AU - Li, Wenxia

AU - Wang, Zhiqiang

PY - 2024

Y1 - 2024

N2 - For let be a self-similar set generated by the iterated function system. Given, let be the set of such that. In this paper we show that is a topological Cantor set having zero Lebesgue measure and full Hausdorff dimension. Furthermore, we show that for any there exists a full Hausdorff dimensional set of such that.

AB - For let be a self-similar set generated by the iterated function system. Given, let be the set of such that. In this paper we show that is a topological Cantor set having zero Lebesgue measure and full Hausdorff dimension. Furthermore, we show that for any there exists a full Hausdorff dimensional set of such that.

KW - Cantor set

KW - Hausdorff dimension

KW - intersection

KW - self-similar set

KW - thickness

UR - https://www.scopus.com/pages/publications/85194968192

U2 - 10.1017/prm.2024.66

DO - 10.1017/prm.2024.66

M3 - 文章

AN - SCOPUS:85194968192

SN - 0308-2105

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

ER -

On a class of self-similar sets which contain finitely many common points

Abstract

Keywords

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