Diophantine approximation of the orbit of 1 in the dynamical system of beta expansions
Li, Bing ; Persson, Tomas LU
; Wang, Baowei
and Wu, Jun
(2014)
In Mathematische Zeitschrift
276(3-4).
p.799-827
- Abstract
- We consider the distribution of the orbits of the number 1 under the -transformations as varies. Mainly, the size of the set of for which a given point can be well approximated by the orbit of 1 is measured by its Hausdorff dimension. The dimension of the following set is determined, where is a given point in and is a sequence of integers tending to infinity as . For the proof of this result, the notion of the recurrence time of a word in symbolic space is introduced to characterise the lengths and the distribution of cylinders (the set of with a common prefix in the expansion of 1) in the parameter space .
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4410957
- author
- Li, Bing
; Persson, Tomas
LU
; Wang, Baowei
and Wu, Jun
- organization
- publishing date
- 2014
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- beta-expansion, Diophantine approximation, Hausdorff dimension
- in
- Mathematische Zeitschrift
- volume
- 276
- issue
- 3-4
- pages
- 799 - 827
- publisher
- Springer
- external identifiers
-
- wos:000332835800009
- scopus:84897647951
- ISSN
- 0025-5874
- DOI
- 10.1007/s00209-013-1223-0
- language
- English
- LU publication?
- yes
- id
- fa8f996e-2aab-4ba2-ba55-e3563c0365b5 (old id 4410957)
- alternative location
- https://arxiv.org/abs/1301.3595
- date added to LUP
- 2016-04-01 09:58:01
- date last changed
- 2022-01-25 18:32:18
@article{fa8f996e-2aab-4ba2-ba55-e3563c0365b5,
abstract = {{We consider the distribution of the orbits of the number 1 under the -transformations as varies. Mainly, the size of the set of for which a given point can be well approximated by the orbit of 1 is measured by its Hausdorff dimension. The dimension of the following set is determined, where is a given point in and is a sequence of integers tending to infinity as . For the proof of this result, the notion of the recurrence time of a word in symbolic space is introduced to characterise the lengths and the distribution of cylinders (the set of with a common prefix in the expansion of 1) in the parameter space .}},
author = {{Li, Bing and Persson, Tomas and Wang, Baowei and Wu, Jun}},
issn = {{0025-5874}},
keywords = {{beta-expansion; Diophantine approximation; Hausdorff dimension}},
language = {{eng}},
number = {{3-4}},
pages = {{799--827}},
publisher = {{Springer}},
series = {{Mathematische Zeitschrift}},
title = {{Diophantine approximation of the orbit of 1 in the dynamical system of beta expansions}},
url = {{http://dx.doi.org/10.1007/s00209-013-1223-0}},
doi = {{10.1007/s00209-013-1223-0}},
volume = {{276}},
year = {{2014}},
}