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Shrinking targets in parametrised families

Aspenberg, Magnus LU and Persson, Tomas LU (2017) In Mathematical Proceedings of the Cambridge Philosophical Society
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.

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author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
in
Mathematical Proceedings of the Cambridge Philosophical Society
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
date added to LUP
2018-01-04 09:52:05
date last changed
2018-01-04 09:52:05
@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},
  month        = {11},
  pages        = {31},
  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},
  year         = {2017},
}