Arkiv för Matematik

On the dynamics of composite entire functions

Walter Bergweiler and Yuefei Wang

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Abstract

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 zC, then z∈ℐ8464 (f⊗g) if and only if g(z)∈ℐ8464 (g⊗f); if U is a component of F(fg) and V is the component of F(gg) 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.

Note

The second author was supported by Max-Planck-Gessellschaft ZFDW, and by Tian Yuan Foundation, NSFC.

Article information

Source
Ark. Mat. Volume 36, Number 1 (1998), 31-39.

Dates
Received: 28 February 1997
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898579

Digital Object Identifier
doi:10.1007/BF02385665

Zentralblatt MATH identifier
0906.30025

Rights
1998 © Institut Mittag-Leffler

Citation

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.


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