Slowly recurrent Collet–Eckmann maps on the Riemann sphere
(2024) In Mathematische Annalen- Abstract
In this paper we study perturbations of rational Collet–Eckmann maps for which the Julia set is the whole sphere, and for which the critical set is allowed to be slowly recurrent. Generically, if each critical point is simple, we show that each such Collet–Eckmann map is a Lebesgue point of Collet–Eckmann maps in the space of rational maps of the same degree d≥ 2 . The same result holds in each subspace, where we fix the multiplicities of the critical points.
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https://lup.lub.lu.se/record/b4618615-5f48-4c26-8c7e-01b6b0bb97c5
- author
- Aspenberg, Magnus LU
- organization
- publishing date
- 2024
- type
- Contribution to journal
- publication status
- epub
- subject
- in
- Mathematische Annalen
- publisher
- Springer
- external identifiers
-
- scopus:85183924644
- ISSN
- 0025-5831
- DOI
- 10.1007/s00208-024-02800-4
- language
- English
- LU publication?
- yes
- id
- b4618615-5f48-4c26-8c7e-01b6b0bb97c5
- date added to LUP
- 2024-02-26 13:52:01
- date last changed
- 2024-02-26 13:53:25
@article{b4618615-5f48-4c26-8c7e-01b6b0bb97c5,
abstract = {{<p>In this paper we study perturbations of rational Collet–Eckmann maps for which the Julia set is the whole sphere, and for which the critical set is allowed to be slowly recurrent. Generically, if each critical point is simple, we show that each such Collet–Eckmann map is a Lebesgue point of Collet–Eckmann maps in the space of rational maps of the same degree d≥ 2 . The same result holds in each subspace, where we fix the multiplicities of the critical points.</p>}},
author = {{Aspenberg, Magnus}},
issn = {{0025-5831}},
language = {{eng}},
publisher = {{Springer}},
series = {{Mathematische Annalen}},
title = {{Slowly recurrent Collet–Eckmann maps on the Riemann sphere}},
url = {{http://dx.doi.org/10.1007/s00208-024-02800-4}},
doi = {{10.1007/s00208-024-02800-4}},
year = {{2024}},
}