Non-existence of
  absolutely continuous invariant probabilities for exponential maps

Neil Dobbs; Bart/lomiej Skorulski

doi:10.4064/fm198-3-6

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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.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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

Affiliations des auteurs :

Neil Dobbs ¹ ; Bart/lomiej Skorulski ²

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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. http://geodesic.mathdoc.fr/articles/10.4064/fm198-3-6/

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