Perturbations of exponential maps : Non-recurrent dynamics
(2024) In Journal d'Analyse Mathematique 153(2). p.759-775- Abstract
We study perturbations of non-recurrent parameters in the exponential family. It is shown that the set of such parameters has Lebesgue measure zero. This particularly implies that the set of escaping parameters has Lebesgue measure zero, which complements a result of Qiu from 1994. Moreover, we show that non-recurrent parameters can be approximated by hyperbolic ones.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/690a883d-813a-4b94-9cc5-c7c42c9611ed
- author
- Aspenberg, Magnus LU and Cui, Weiwei LU
- organization
- publishing date
- 2024-09
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal d'Analyse Mathematique
- volume
- 153
- issue
- 2
- pages
- 17 pages
- publisher
- Magnes Press
- external identifiers
-
- scopus:85204155738
- ISSN
- 0021-7670
- DOI
- 10.1007/s11854-024-0340-5
- language
- English
- LU publication?
- yes
- id
- 690a883d-813a-4b94-9cc5-c7c42c9611ed
- date added to LUP
- 2024-12-02 13:37:13
- date last changed
- 2025-04-04 14:00:34
@article{690a883d-813a-4b94-9cc5-c7c42c9611ed,
abstract = {{<p>We study perturbations of non-recurrent parameters in the exponential family. It is shown that the set of such parameters has Lebesgue measure zero. This particularly implies that the set of escaping parameters has Lebesgue measure zero, which complements a result of Qiu from 1994. Moreover, we show that non-recurrent parameters can be approximated by hyperbolic ones.</p>}},
author = {{Aspenberg, Magnus and Cui, Weiwei}},
issn = {{0021-7670}},
language = {{eng}},
number = {{2}},
pages = {{759--775}},
publisher = {{Magnes Press}},
series = {{Journal d'Analyse Mathematique}},
title = {{Perturbations of exponential maps : Non-recurrent dynamics}},
url = {{http://dx.doi.org/10.1007/s11854-024-0340-5}},
doi = {{10.1007/s11854-024-0340-5}},
volume = {{153}},
year = {{2024}},
}