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CONSTRUCTING HERMAN RINGS BY TWISTING ANNULUS HOMEOMORPHISMS

Published online by Cambridge University Press:  01 February 2009

XIUMEI WANG
Affiliation:
Department of Computer Science and Information Technology, JiangSu Teachers University of Technology, Changzhou, 213001, PR China (email: [email protected])
GAOFEI ZHANG*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, 210093, PR China (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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Let F(z) be a rational map with degree at least three. Suppose that there exists an annulus such that (1) H separates two critical points of F, and (2) F:HF(H) is a homeomorphism. Our goal in this paper is to show how to construct a rational map G by twisting F on H such that G has the same degree as F and, moreover, G has a Herman ring with any given Diophantine type rotation number.

Keywords

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The second author is partially supported by NJU-0203005116.

References

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