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Slowly recurrent Collet–Eckmann maps with non-empty Fatou set

Aspenberg, Magnus LU ; Bylund, Mats LU and Cui, Weiwei LU (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:
author
; and
organization
publishing date
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}},
}