Some pinching deformations of the Fatou function

Patricia Domínguez, and Guillermo Sienra. "Some pinching deformations of the Fatou function." Fundamenta Mathematicae 228.1 (2015): 1-15. <http://eudml.org/doc/283031>.

@article{PatriciaDomínguez2015,
abstract = {We are interested in deformations of Baker domains by a pinching process in curves. In this paper we deform the Fatou function $F(z) = z + 1 + e^\{-z\}$, depending on the curves selected, to any map of the form $F_\{p/q\}(z) = z + e^\{-z\} + 2πip/q$, p/q a rational number. This process deforms a function with a doubly parabolic Baker domain into a function with an infinite number of doubly parabolic periodic Baker domains if p = 0, otherwise to a function with wandering domains. Finally, we show that certain attracting domains can be deformed by a pinching process into doubly parabolic Baker domains.},
author = {Patricia Domínguez, Guillermo Sienra},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {1},
pages = {1-15},
title = {Some pinching deformations of the Fatou function},
url = {http://eudml.org/doc/283031},
volume = {228},
year = {2015},
}

TY - JOUR
AU - Patricia Domínguez
AU - Guillermo Sienra
TI - Some pinching deformations of the Fatou function
JO - Fundamenta Mathematicae
PY - 2015
VL - 228
IS - 1
SP - 1
EP - 15
AB - We are interested in deformations of Baker domains by a pinching process in curves. In this paper we deform the Fatou function $F(z) = z + 1 + e^{-z}$, depending on the curves selected, to any map of the form $F_{p/q}(z) = z + e^{-z} + 2πip/q$, p/q a rational number. This process deforms a function with a doubly parabolic Baker domain into a function with an infinite number of doubly parabolic periodic Baker domains if p = 0, otherwise to a function with wandering domains. Finally, we show that certain attracting domains can be deformed by a pinching process into doubly parabolic Baker domains.
LA - eng
UR - http://eudml.org/doc/283031
ER -