Shrinking targets in parametrised families
Aspenberg, Magnus LU and Persson, Tomas LU
(2019)
In Mathematical Proceedings of the Cambridge Philosophical Society
166(2).
p.265-295
- Abstract
We consider certain parametrised families of piecewise expanding maps on the interval, and estimate and sometimes calculate the Hausdorff dimension of the set of parameters for which the orbit of a fixed point has a certain shrinking target property. This generalises several similar results for β-transformations to more general non-linear families. The proofs are based on a result by Schnellmann on typicality in parametrised families.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/ff793ce1-0894-4b88-8de4-0016c1c46553
- author
- Aspenberg, Magnus
LU
and Persson, Tomas
LU
- organization
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Mathematical Proceedings of the Cambridge Philosophical Society
- volume
- 166
- issue
- 2
- pages
- 31 pages
- publisher
- Cambridge University Press
- external identifiers
-
- scopus:85038236734
- ISSN
- 0305-0041
- DOI
- 10.1017/S0305004117000822
- language
- English
- LU publication?
- yes
- id
- ff793ce1-0894-4b88-8de4-0016c1c46553
- alternative location
- https://arxiv.org/abs/1603.01116
- date added to LUP
- 2018-01-04 09:52:05
- date last changed
- 2022-04-25 04:45:38
@article{ff793ce1-0894-4b88-8de4-0016c1c46553,
abstract = {{<p>We consider certain parametrised families of piecewise expanding maps on the interval, and estimate and sometimes calculate the Hausdorff dimension of the set of parameters for which the orbit of a fixed point has a certain shrinking target property. This generalises several similar results for β-transformations to more general non-linear families. The proofs are based on a result by Schnellmann on typicality in parametrised families.</p>}},
author = {{Aspenberg, Magnus and Persson, Tomas}},
issn = {{0305-0041}},
language = {{eng}},
number = {{2}},
pages = {{265--295}},
publisher = {{Cambridge University Press}},
series = {{Mathematical Proceedings of the Cambridge Philosophical Society}},
title = {{Shrinking targets in parametrised families}},
url = {{http://dx.doi.org/10.1017/S0305004117000822}},
doi = {{10.1017/S0305004117000822}},
volume = {{166}},
year = {{2019}},
}