Non-existence of absolutely continuous invariant probabilities for exponential maps
Dynamical Systems
2009-02-18 v4
Abstract
We show that for entire maps of the form such that the orbit of zero is bounded and such that Lebesgue almost every point is transitive, no absolutely continuous invariant probability measure can exist. This answers a long-standing open problem.
Cite
@article{arxiv.0801.0075,
title = {Non-existence of absolutely continuous invariant probabilities for exponential maps},
author = {Neil Dobbs and Bartlomiej Skorulski},
journal= {arXiv preprint arXiv:0801.0075},
year = {2009}
}
Comments
4 pages. Similar to the version published in Fundamenta in February 2008