Non-existence of absolutely continuous invariant probabilities for exponential maps
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
We show that for entire maps of the form $z \mapsto λ\exp(z)$ 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.
4 pages. Similar to the version published in Fundamenta in February 2008
4 pages. Similar to the version published in Fundamenta in February 2008