Speiser Meets Misiurewicz
(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:
https://lup.lub.lu.se/record/99813af9-01c4-4933-8d0e-1c9ef68395d1
- author
- Aspenberg, Magnus LU and Cui, Weiwei LU
- organization
- publishing date
- 2024-02
- 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}}, }