Recurrence of entire transcendental functions with simple post-singular sets

• Autorzy: Jan-Martin Hemke
• Języki publikacji: EN

Abstrakty

EN

We study how the orbits of the singularities of the inverse of a meromorphic function determine the dynamics on its Julia set, at least up to a set of (Lebesgue) measure zero. We concentrate on a family of entire transcendental functions with only finitely many singularities of the inverse, counting multiplicity, all of which either escape exponentially fast or are pre-periodic. For these functions we are able to decide whether the function is recurrent or not. In the case that the Julia set is not the entire plane we also obtain estimates for the measure of the Julia set.

Kategorie tematyczne

• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 187
• Numer: 3
• Strony: 255-289

Daty

wydano

2005

Twórcy

autor

Jan-Martin Hemke

• Mathematisches Institut der, Christian-Albrechts-Universität zu Kiel, Ludwig-Meyn-Str. 4, 24118 Kiel, Germany

Identyfikatory

DOI

10.4064/fm187-3-4