Non-existence of absolutely continuous invariant probabilities for exponential maps
Neil Dobbs ; Bartłomiej Skorulski
Fundamenta Mathematicae, Tome 201 (2008), p. 283-287 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:282613 
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Neil Dobbs; Bartłomiej Skorulski. Non-existence of absolutely continuous invariant probabilities for exponential maps. Fundamenta Mathematicae, Tome 201 (2008) pp. 283-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-3-6/