Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Walter Bergweiler,Kiel University, Germany
Inviter:
数学所
Title:
Hyperbolic entire functions
Time & Venue:
2014.9.24 3:30pm 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:
Appendix:
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