Non-existence of absolutely continuous invariant probabilities for exponential maps
Neil Dobbs; Bartłomiej Skorulski
Fundamenta Mathematicae (2008)
- Volume: 198, Issue: 3, page 283-287
- ISSN: 0016-2736
Access Full Article
top
Abstract
topHow to cite
topNeil Dobbs, and Bartłomiej Skorulski. "Non-existence of absolutely continuous invariant probabilities for exponential maps." Fundamenta Mathematicae 198.3 (2008): 283-287. <http://eudml.org/doc/282613>.
@article{NeilDobbs2008,
abstract = {We show that for entire maps of the form z ↦ λexp(z) such that the orbit of zero is bounded and Lebesgue almost every point is transitive, no absolutely continuous invariant probability measure can exist. This answers a long-standing open problem.},
author = {Neil Dobbs, Bartłomiej Skorulski},
journal = {Fundamenta Mathematicae},
keywords = {exponential maps; absolutely continuous invariant probability measures; nice sets},
language = {eng},
number = {3},
pages = {283-287},
title = {Non-existence of absolutely continuous invariant probabilities for exponential maps},
url = {http://eudml.org/doc/282613},
volume = {198},
year = {2008},
}
TY - JOUR
AU - Neil Dobbs
AU - Bartłomiej Skorulski
TI - Non-existence of absolutely continuous invariant probabilities for exponential maps
JO - Fundamenta Mathematicae
PY - 2008
VL - 198
IS - 3
SP - 283
EP - 287
AB - We show that for entire maps of the form z ↦ λexp(z) such that the orbit of zero is bounded and Lebesgue almost every point is transitive, no absolutely continuous invariant probability measure can exist. This answers a long-standing open problem.
LA - eng
KW - exponential maps; absolutely continuous invariant probability measures; nice sets
UR - http://eudml.org/doc/282613
ER -
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.