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Speiser meets Misiurewicz
- Source :
- Comm. Math. Phys. 405 (2024), no. 2, Paper No. 55
- Publication Year :
- 2022
-
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.<br />Comment: 37 pages, 1 figure. Author accepted version. Overall revision on Section 2 and Section 4. To appear in Communications in Mathematical Physics
- Subjects :
- Mathematics - Dynamical Systems
Mathematics - Complex Variables
37F10, 30D05
Subjects
Details
- Database :
- arXiv
- Journal :
- Comm. Math. Phys. 405 (2024), no. 2, Paper No. 55
- Publication Type :
- Report
- Accession number :
- edsarx.2209.00385
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00220-024-04945-4