Arkiv för Matematik
- Ark. Mat.
- Volume 36, Number 1 (1998), 31-39.
On the dynamics of composite entire functions
Letf and g be nonlinear entire functions. The relations between the dynamics of f⊗g and g⊗f are discussed. Denote byℐ (·) and F(·) the Julia and Fatou sets. It is proved that if z∈C, then z∈ℐ8464 (f⊗g) if and only if g(z)∈ℐ8464 (g⊗f); if U is a component of F(f○g) and V is the component of F(g○g) that contains g(U), then U is wandering if and only if V is wandering; if U is periodic, then so is V and moreover, V is of the same type according to the classification of periodic components as U. These results are used to show that certain new classes of entire functions do not have wandering domains.
The second author was supported by Max-Planck-Gessellschaft ZFDW, and by Tian Yuan Foundation, NSFC.
Ark. Mat. Volume 36, Number 1 (1998), 31-39.
Received: 28 February 1997
First available in Project Euclid: 31 January 2017
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1998 © Institut Mittag-Leffler
Bergweiler, Walter; Wang, Yuefei. On the dynamics of composite entire functions. Ark. Mat. 36 (1998), no. 1, 31--39. doi:10.1007/BF02385665. https://projecteuclid.org/euclid.afm/1485898579.