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Shrinking targets and eventually always hitting points for interval maps

Kirsebom, Maxim ; Kunde, Philipp and Persson, Tomas LU orcid (2020) In Nonlinearity 33(2). p.892-914
Abstract

We study shrinking target problems and the set of eventually always hitting points. These are the points whose first n iterates will never have empty intersection with the nth target for sufficiently large n. We derive necessary and sufficient conditions on the shrinking rate of the targets for to be of full or zero measure especially for some interval maps including the doubling map, some quadratic maps and the Manneville-Pomeau map. We also obtain results for the Gauß map and correspondingly for the maximal digits in continued fraction expansions. In the case of-Transformations we also compute the packing dimension of complementing already known results on the Hausdorff dimension of.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Nonlinearity
volume
33
issue
2
pages
23 pages
publisher
London Mathematical Society / IOP Science
external identifiers
  • scopus:85082409210
ISSN
0951-7715
DOI
10.1088/1361-6544/ab5160
language
English
LU publication?
yes
id
acc0b76f-41c0-4d7c-80d6-52174dbb0568
date added to LUP
2021-01-11 13:07:24
date last changed
2022-04-26 23:13:55
@article{acc0b76f-41c0-4d7c-80d6-52174dbb0568,
  abstract     = {{<p>We study shrinking target problems and the set of eventually always hitting points. These are the points whose first n iterates will never have empty intersection with the nth target for sufficiently large n. We derive necessary and sufficient conditions on the shrinking rate of the targets for to be of full or zero measure especially for some interval maps including the doubling map, some quadratic maps and the Manneville-Pomeau map. We also obtain results for the Gauß map and correspondingly for the maximal digits in continued fraction expansions. In the case of-Transformations we also compute the packing dimension of complementing already known results on the Hausdorff dimension of.</p>}},
  author       = {{Kirsebom, Maxim and Kunde, Philipp and Persson, Tomas}},
  issn         = {{0951-7715}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{892--914}},
  publisher    = {{London Mathematical Society / IOP Science}},
  series       = {{Nonlinearity}},
  title        = {{Shrinking targets and eventually always hitting points for interval maps}},
  url          = {{http://dx.doi.org/10.1088/1361-6544/ab5160}},
  doi          = {{10.1088/1361-6544/ab5160}},
  volume       = {{33}},
  year         = {{2020}},
}