Geodesic
Non-existence of absolutely continuous invariant probabilities for exponential maps
Neil Dobbs 1   ; Bart/lomiej Skorulski 2
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 P.O. Box 21, 00-956 Warszawa, Poland
2 Departamento de Matemáticas Universidad Católica del Norte Avenida Angamos 0610 Casilla 1280, Antofagasta, Chile
Fundamenta Mathematicae, Tome 198 (2008) no. 3, pp. 283-287 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that for entire maps of the form $z \mapsto \lambda \exp(z)$ 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.
DOI : 10.4064/fm198-3-6
Keywords: entire maps form mapsto lambda exp orbit zero bounded lebesgue almost every point transitive absolutely continuous invariant probability measure exist answers long standing problem

Neil Dobbs  1   ; Bart/lomiej Skorulski  2

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 P.O. Box 21, 00-956 Warszawa, Poland
2 Departamento de Matemáticas Universidad Católica del Norte Avenida Angamos 0610 Casilla 1280, Antofagasta, Chile 
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Neil Dobbs; Bart/lomiej Skorulski. Non-existence of
  absolutely continuous invariant probabilities for exponential maps. Fundamenta Mathematicae, Tome 198 (2008) no. 3, pp. 283-287. doi: 10.4064/fm198-3-6

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