Gap sequences of McMullen sets
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- by Jun Jie Miao, Li-Feng Xi and Ying Xiong PDF
- Proc. Amer. Math. Soc. 145 (2017), 1629-1637 Request permission
Abstract:
We study the gap sequence of totally disconnected McMullen sets. Our result shows that if every horizontal line in the McMullen set is nonempty, then the gap sequence is unrelated to the box dimension. This implies that in such situations, the separation properties of McMullen sets are quite different from that of self-similar sets.References
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Additional Information
- Jun Jie Miao
- Affiliation: Shanghai Key Laboratory of PMMP, Department of Mathematics, East China Normal University, No. 500, Dongchuan Road, Shanghai 200241, People’s Republic of China
- Email: jjmiao@math.ecnu.edu.cn
- Li-Feng Xi
- Affiliation: Department of Mathematics, Ningbo University, Ningbo 315211, People’s Republic of China
- Email: xilifengningbo@yahoo.com
- Ying Xiong
- Affiliation: Department of Mathematics, South China University of Technology, Guangzhou, 510641, People’s Republic of China
- MR Author ID: 808546
- Email: xiongyng@gmail.com
- Received by editor(s): June 7, 2015
- Received by editor(s) in revised form: June 5, 2016
- Published electronically: November 21, 2016
- Additional Notes: The authors were supported by National Natural Science Foundation of China (Grants No. 11201152, 11371329, 11471124), NSF of Zhejiang Province (No. LR13A010001), the Fund for the Doctoral Program of Higher Education of China 20120076120001 and Morningside Center of Mathematics.
- Communicated by: Kevin Whyte
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1629-1637
- MSC (2010): Primary 28A80
- DOI: https://doi.org/10.1090/proc/13342
- MathSciNet review: 3601553