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Trees associated with the configuration of Herman rings

Published online by Cambridge University Press:  19 September 2008

Mitshuhiro Shishikura
Mitshuhiro Shishikura
Affiliation:
Department of Mathematics, Kyoto University, Kyoto, 606, Japan†
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Abstract

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For a rational function with Herman rings, we define a tree and a piece-wise linear map on it, which reflect the configuration of the Herman rings. Their properties are investigated and some examples are given. Moreover, it is possible to define a similar tree associated with (super) attractive basins or Siegel disks.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 3 , September 1989 , pp. 543 - 560
Copyright
Copyright © Cambridge University Press 1989

References

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