Amb motiu del tancament d'estiu, la validació de documents es reprendrà a partir del 28 d'agost de 2026. Disculpeu les molèsties.
Con motivo del cierre de verano, la validación de documentos se reanudará a partir del 28 de agosto de 2026. Disculpad las molestias
Due to the summer closure, document validation will resume starting August 28, 2026. We apologize for any inconvenience.

Files

670246.pdf (399.43 KB)

Document type

Article

Version

Accepted version

Publication date

2019

All rights reserved

Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/164077

Escaping points in the boundaries of baker domains

Journal Title

Authors

Director/Tutor

Journal ISSN

Volume Title

Related resource

https://doi.org/10.1007/s11854-019-0011-0

Abstract

We study the dynamical behaviour of points in the boundaries of simply connected invariant Baker domains $U$ of meromorphic maps $f$ with a finite degree on $U$. We prove that if $f|_U$ is of hyperbolic or simply parabolic type, then almost every point in the boundary of $U$, with respect to harmonic measure, escapes to infinity under iteration of $f$. On the contrary, if $f|_U$ is of doubly parabolic type, then almost every point in the boundary of $U$, with respect to harmonic measure, has dense forward trajectory in the boundary of $U$, in particular the set of escaping points in the boundary of $U$ has harmonic measure zero. We also present some extensions of the results to the case when $f$ has infinite degree on $U$, including classical Fatou example.

Subject

Funcions de variables complexes, Sistemes dinàmics complexos, Funcions meromorfes

Subject (English)

Functions of complex variables, Complex dynamical systems, Meromorphic functions

Citation

Collections

Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

BARANSKI, Krzysztof, et al. Escaping points in the boundaries of baker domains. Journal d'Analyse Mathematique. 2019. Vol. 137, num. 2, pags. 679-706. ISSN 0021-7670. [consulted: 16 of August of 2026]. Available at: https://hdl.handle.net/2445/164077

Export metadata

JSON - METS

Share record