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Hyperbolic entire functions
【2014.9.24 3:30pm, N202】

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 2014-9-19 

  Colloquia & Seminars 

  Speaker

Prof. Walter Bergweiler,Kiel University, Germany

  Title

Hyperbolic entire functions

  Time

2014.9.24 3:30pm

  Venue

N202

  Abstract

We show that an invariant Fatou component of a hyperbolic transcendental entire function is a bounded 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 results are optimal. A particularly strong dichotomy is obtained in the case of a function with precisely two critical values. 

  Affiliation

 

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