On eventually always hitting points
(2021) In Monatshefte fur Mathematik 196(4). p.763-784- Abstract
We consider dynamical systems (X, T, μ) which have exponential decay of correlations for either Hölder continuous functions or functions of bounded variation. Given a sequence of balls (Bn)n=1∞, we give sufficient conditions for the set of eventually always hitting points to be of full measure. This is the set of points x such that for all large enough m, there is a k< m with Tk(x) ∈ Bm. We also give an asymptotic estimate as m→ ∞ on the number of k< m with Tk(x) ∈ Bm. As an application, we prove for almost every point x an asymptotic estimate on the number of k≤ m such that ak≥ mt, where t∈ (0 , 1) and ak are the continued fraction coefficients of x.
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https://lup.lub.lu.se/record/ba79b8c5-fa33-46c0-ad5c-f56d2f4af7a3
- author
- Ganotaki, Charis LU and Persson, Tomas LU
- organization
- publishing date
- 2021-08-28
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Continued fractions, Eventually always hitting points, Shrinking targets
- in
- Monatshefte fur Mathematik
- volume
- 196
- issue
- 4
- pages
- 763 - 784
- publisher
- Springer
- external identifiers
-
- scopus:85113817998
- ISSN
- 0026-9255
- DOI
- 10.1007/s00605-021-01616-7
- language
- English
- LU publication?
- yes
- id
- ba79b8c5-fa33-46c0-ad5c-f56d2f4af7a3
- date added to LUP
- 2021-09-27 13:06:54
- date last changed
- 2022-04-27 04:15:46
@article{ba79b8c5-fa33-46c0-ad5c-f56d2f4af7a3, abstract = {{<p>We consider dynamical systems (X, T, μ) which have exponential decay of correlations for either Hölder continuous functions or functions of bounded variation. Given a sequence of balls (Bn)n=1∞, we give sufficient conditions for the set of eventually always hitting points to be of full measure. This is the set of points x such that for all large enough m, there is a k< m with T<sup>k</sup>(x) ∈ B<sub>m</sub>. We also give an asymptotic estimate as m→ ∞ on the number of k< m with T<sup>k</sup>(x) ∈ B<sub>m</sub>. As an application, we prove for almost every point x an asymptotic estimate on the number of k≤ m such that a<sub>k</sub>≥ m<sup>t</sup>, where t∈ (0 , 1) and a<sub>k</sub> are the continued fraction coefficients of x.</p>}}, author = {{Ganotaki, Charis and Persson, Tomas}}, issn = {{0026-9255}}, keywords = {{Continued fractions; Eventually always hitting points; Shrinking targets}}, language = {{eng}}, month = {{08}}, number = {{4}}, pages = {{763--784}}, publisher = {{Springer}}, series = {{Monatshefte fur Mathematik}}, title = {{On eventually always hitting points}}, url = {{http://dx.doi.org/10.1007/s00605-021-01616-7}}, doi = {{10.1007/s00605-021-01616-7}}, volume = {{196}}, year = {{2021}}, }