Non-recurrent meromorphic functions

Jacek Graczyk, Janina Kotus, and Grzegorz Świątek. "Non-recurrent meromorphic functions." Fundamenta Mathematicae 182.3 (2004): 269-281. <http://eudml.org/doc/282911>.

@article{JacekGraczyk2004,
abstract = {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.},
author = {Jacek Graczyk, Janina Kotus, Grzegorz Świątek},
journal = {Fundamenta Mathematicae},
keywords = {transcendental meromorphic function; Julia set; postcritical set; critical points; invariant set},
language = {eng},
number = {3},
pages = {269-281},
title = {Non-recurrent meromorphic functions},
url = {http://eudml.org/doc/282911},
volume = {182},
year = {2004},
}

TY - JOUR
AU - Jacek Graczyk
AU - Janina Kotus
AU - Grzegorz Świątek
TI - Non-recurrent meromorphic functions
JO - Fundamenta Mathematicae
PY - 2004
VL - 182
IS - 3
SP - 269
EP - 281
AB - 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.
LA - eng
KW - transcendental meromorphic function; Julia set; postcritical set; critical points; invariant set
UR - http://eudml.org/doc/282911
ER -