ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 30, 58 KISAKA, Masashi, Osaka Prefecture University, JAPAN On the Connnected Components of Julia Sets of Transcendental Entire Functions Let f : C → C be an transcendental entire function and J(f) ⊂ C its Julia set. We shall show that all the connected components of J(f) are unbounded if and only if f has no multiply-connected wandering domains, and all the connected components of J(f) are bounded if and only if f has a multiply-connected wandering domains. Consequently there is no possibility of coexistence of bounded components and unbounded components. We shall also refer to some properties of buried components.