Non-existence of absolutely continuous invariant probabilities for exponential maps

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dc.creatorDobbs, Neil
dc.creatorSkorulski, Bartlomiej
dc.date2007-12-30
dc.date2009-02-18
dc.date.accessioned2026-07-07T12:42:27Z
dc.date.available2026-07-07T12:42:27Z
dc.descriptionWe 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.
dc.description4 pages. Similar to the version published in Fundamenta in February 2008
dc.identifierhttps://arxiv.org/abs/0801.0075
dc.identifierhttp://arxiv.org/abs/0801.0075
dc.identifierFundamenta Mathematicae, 198(3):283-287, 2008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220083
dc.subjectDynamical Systems
dc.subject37F10
dc.titleNon-existence of absolutely continuous invariant probabilities for exponential maps
dc.typetext

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