A+ CATEGORY SCIENTIFIC UNIT

Non-existence of absolutely continuous invariant probabilities for exponential maps

Volume 198 / 2008

Neil Dobbs, Bart/lomiej Skorulski Fundamenta Mathematicae 198 (2008), 283-287 MSC: Primary 37F10. DOI: 10.4064/fm198-3-6

Abstract

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.

Authors

  • Neil DobbsInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    P.O. Box 21, 00-956 Warszawa, Poland
    e-mail
  • Bart/lomiej SkorulskiDepartamento de Matemáticas
    Universidad Católica del Norte
    Avenida Angamos 0610
    Casilla 1280, Antofagasta, Chile
    e-mail

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