Non-recurrent meromorphic functions

• Autorzy: Jacek Graczyk , Janina Kotus , Grzegorz Świątek
• Języki publikacji: EN

Abstrakty

EN

We consider a transcendental meromorphic function f belonging to the class ℬ (with bounded set of singular values). We show that if the Julia set J(f) is the whole complex plane ℂ, and the closure of the postcritical set P(f) is contained in B(0,R) ∪ {∞} and is disjoint from the set Crit(f) of critical points, then every compact and forward invariant set is hyperbolic, provided that it is disjoint from Crit(f). It is further shown, under general additional hypotheses, that f admits no measurable invariant line-field.

Kategorie tematyczne

• 37F50: Small divisors, rotation domains and linearization; Fatou and Julia sets
• 30D05: Functional equations in the complex domain, iteration and composition of analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 182
• Numer: 3
• Strony: 269-281

Daty

wydano

2004

Twórcy

autor

Jacek Graczyk

• Département de Mathématiques, Université de Paris-Sud, 91405 Orsay, France

autor

Janina Kotus

• Department of Mathematics, Warsaw University of Technology, 00-661 Warszawa, Poland

autor

Grzegorz Świątek

• Department of Mathematics, Penn State University, University Park, PA 16802, U.S.A.

Identyfikatory

DOI

10.4064/fm182-3-5