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Speiser Meets Misiurewicz

Aspenberg, Magnus LU and Cui, Weiwei LU (2024) In Communications in Mathematical Physics 405(2).
Abstract

We propose a notion of Misiurewicz condition for transcendental entire functions and study perturbations of Speiser functions satisfying this condition in their parameter spaces (in the sense of Eremenko and Lyubich). We show that every Misiurewicz entire function can be approximated by hyperbolic maps in the same parameter space. Moreover, Misiurewicz functions are Lebesgue density points of hyperbolic maps if their Julia sets have zero Lebesgue measure. We also prove that the set of Misiurewicz Speiser functions has Lebesgue measure zero in the parameter space.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
37F10 || 30D05
in
Communications in Mathematical Physics
volume
405
issue
2
article number
55
publisher
Springer
external identifiers
  • scopus:85185678450
ISSN
0010-3616
DOI
10.1007/s00220-024-04945-4
language
English
LU publication?
yes
id
99813af9-01c4-4933-8d0e-1c9ef68395d1
date added to LUP
2024-03-25 15:16:35
date last changed
2024-03-25 15:17:52
@article{99813af9-01c4-4933-8d0e-1c9ef68395d1,
  abstract     = {{<p>We propose a notion of Misiurewicz condition for transcendental entire functions and study perturbations of Speiser functions satisfying this condition in their parameter spaces (in the sense of Eremenko and Lyubich). We show that every Misiurewicz entire function can be approximated by hyperbolic maps in the same parameter space. Moreover, Misiurewicz functions are Lebesgue density points of hyperbolic maps if their Julia sets have zero Lebesgue measure. We also prove that the set of Misiurewicz Speiser functions has Lebesgue measure zero in the parameter space.</p>}},
  author       = {{Aspenberg, Magnus and Cui, Weiwei}},
  issn         = {{0010-3616}},
  keywords     = {{37F10 || 30D05}},
  language     = {{eng}},
  number       = {{2}},
  publisher    = {{Springer}},
  series       = {{Communications in Mathematical Physics}},
  title        = {{Speiser Meets Misiurewicz}},
  url          = {{http://dx.doi.org/10.1007/s00220-024-04945-4}},
  doi          = {{10.1007/s00220-024-04945-4}},
  volume       = {{405}},
  year         = {{2024}},
}