Non-existence of absolutely continuous invariant probabilities for exponential maps

Details Non-existence of absolutely continuous invariant probabilities for exponential maps Non-existence of absolutely continuous invariant probabilities for exponential maps

2007-12-30

arxiv.org/abs/0801.0075v4

Fundamenta Mathematicae, 198(3):283-287, 2008

Mathematics

Dynamical Systems

4 pages. Similar to the version published in Fundamenta in February 2008

Scientific paper

We show that for entire maps of the form $z \mapsto \lambda \exp(z)$ 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.

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