Year: 2025
Type: article
Abstract: Let $$ f:\mathbb {C}\rightarrow \widehat{\mathbb {C}} $$ f : C → C ^ be a transcendental map, and let U be an attracting or parabolic basin, or a doubly parabolic Baker domain. Assume U is simply connected. Then, we prove that periodic points are dense in $$ \partial U $$ ∂ U , under certain hypothesis on the postsingular set. This generalizes a result by Przytycki and Zdunik for rational maps (Fund Math 145(1):65–77, 1994). Our proof uses techniques from measure theory, ergodic theory, conformal analysis, and inner functions. In particular, a result on the distortion of inner functions near the unit circle is provided, which is of independent interest.
Source: Mathematische Annalen
Author: Anna Jové
Institution: Universitat de Barcelona
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: G2765657911, G2860071292
OpenAlex ID: W4409686336