Slowly recurrent Collet–Eckmann maps with non-empty Fatou set
(2024) In Proceedings of the London Mathematical Society 128(1).- Abstract
In this paper, we study rational Collet–Eckmann maps for which the Julia set is not the whole sphere and for which the critical points are recurrent at a slow rate. In families where the orders of the critical points are fixed, we prove that such maps are Lebesgue density points of hyperbolic maps. In particular, if all critical points are simple, these maps are Lebesgue density points of hyperbolic maps in the full space of rational maps of any degree (Formula presented.).
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/67dc2636-8391-4064-bf65-e3914364ab09
- author
- Aspenberg, Magnus LU ; Bylund, Mats LU and Cui, Weiwei LU
- organization
- publishing date
- 2024-01
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Proceedings of the London Mathematical Society
- volume
- 128
- issue
- 1
- article number
- e12574
- publisher
- LONDON MATH SOC, BURLINGTON HOUSE PICCADILLY, LONDON, ENGLAND W1V 0NL
- external identifiers
-
- scopus:85180249993
- ISSN
- 0024-6115
- DOI
- 10.1112/plms.12574
- language
- English
- LU publication?
- yes
- id
- 67dc2636-8391-4064-bf65-e3914364ab09
- date added to LUP
- 2024-01-31 14:20:59
- date last changed
- 2024-01-31 14:22:57
@article{67dc2636-8391-4064-bf65-e3914364ab09, abstract = {{<p>In this paper, we study rational Collet–Eckmann maps for which the Julia set is not the whole sphere and for which the critical points are recurrent at a slow rate. In families where the orders of the critical points are fixed, we prove that such maps are Lebesgue density points of hyperbolic maps. In particular, if all critical points are simple, these maps are Lebesgue density points of hyperbolic maps in the full space of rational maps of any degree (Formula presented.).</p>}}, author = {{Aspenberg, Magnus and Bylund, Mats and Cui, Weiwei}}, issn = {{0024-6115}}, language = {{eng}}, number = {{1}}, publisher = {{LONDON MATH SOC, BURLINGTON HOUSE PICCADILLY, LONDON, ENGLAND W1V 0NL}}, series = {{Proceedings of the London Mathematical Society}}, title = {{Slowly recurrent Collet–Eckmann maps with non-empty Fatou set}}, url = {{http://dx.doi.org/10.1112/plms.12574}}, doi = {{10.1112/plms.12574}}, volume = {{128}}, year = {{2024}}, }