On the dynamics of composite entire functions

Walter Bergweiler Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel Yuefei Wang Institute of Mathematics, Academia Sinica

TBD mathscidoc:1701.332882

Arkiv for Matematik, 36, (1), 31-39, 1997.2
Let$f$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.
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  title={On the dynamics of composite entire functions},
  author={Walter Bergweiler, and Yuefei Wang},
  booktitle={Arkiv for Matematik},
Walter Bergweiler, and Yuefei Wang. On the dynamics of composite entire functions. 1997. Vol. 36. In Arkiv for Matematik. pp.31-39. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203551798453691.
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