# name
Hyperbolic entire functions with bounded Fatou components

# metadata.dc.description.abstract[].value
We show that an invariant Fatou component of a hyperbolic transcenden- tal entire function is a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. We use this theorem to prove criteria for the boundedness of Fatou components and local connectivity of Julia sets for hyperbolic entire functions, and give examples that demonstrate that our re- sults are optimal. A particularly strong dichotomy is obtained in the case of a function with precisely two critical values.

# metadata.dc.relation.ispartof[].value
Commentarii Mathematici Helvetici, 2015, vol. 90, num. 4, p. 799-829

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Hyperbolic entire functions with bounded Fatou components