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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

REFERENCES

[A1]Ahlfors, L. V.. Complex Analysis. McGraw-Hill: New York, 1953.Google Scholar
[A2]Ahlfors, L. V.. Lectures on Quasiconformal Mappings. Van Nostrand: New York, 1966.Google Scholar
[B]Blanchard, P.. Complex analytic dynamics on the Riemann sphere. Bull. AMS. 11 (1984), 85–141.Google Scholar
[D]Douady, A.. Disques de Siegel et anneaux de Herman. Séminaire N. Bourbaki, exposé 677 (1986/1987).Google Scholar
[DH]Douady, A. et al. Etudes dynamiques des polynômes complexes I, II. Publ. Math. d'Orsay 84–02 (1984), 85–05 (1985).Google Scholar
[H]Herman, M. R.. Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann. Bull. Soc. Math. France 112 (1984), 93–142.Google Scholar
[S1]Shishikura, M.. On the quasiconformal surgery of the rational functions. Ann. Scient. Ec. Norm. Sup. (4) t.20 (1987), 1–29.Google Scholar
[S2]Shishikura, M.. Construction of Herman rings from trees. In preparation.Google Scholar