Diophantine approximation of the orbit of 1 in the dynamical system of beta expansions
(2014) In Mathematische Zeitschrift 276(34). p.799827 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:
http://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
 betaexpansion, Diophantine approximation, Hausdorff dimension
 in
 Mathematische Zeitschrift
 volume
 276
 issue
 34
 pages
 799  827
 publisher
 Springer
 external identifiers

 wos:000332835800009
 scopus:84897647951
 ISSN
 00255874
 DOI
 10.1007/s0020901312230
 language
 English
 LU publication?
 yes
 id
 fa8f996e2aab4ba2ba55e3563c0365b5 (old id 4410957)
 date added to LUP
 20140429 11:20:58
 date last changed
 20170924 03:03:44
@article{fa8f996e2aab4ba2ba55e3563c0365b5, 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 = {00255874}, keyword = {betaexpansion,Diophantine approximation,Hausdorff dimension}, language = {eng}, number = {34}, pages = {799827}, 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/s0020901312230}, volume = {276}, year = {2014}, }