Extending local analytic conjugacies

Author:
Hiroyuki Inou

Journal:
Trans. Amer. Math. Soc. **363** (2011), 331-343

MSC (2010):
Primary 37F10; Secondary 32B10, 30D05

Published electronically:
August 25, 2010

MathSciNet review:
2719684

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Abstract: We prove that if two globally-defined one-dimensional complex dynamics are locally analytically conjugate, then we extend the conjugacy to obtain global conjugacy by a correspondence. The most important case occurs when two rational maps have analytically conjugate polynomial-like restrictions. In this case, we prove that there exists another rational map which is semiconjugate to them both by some rational maps.

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Additional Information

**Hiroyuki Inou**

Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan

DOI:
https://doi.org/10.1090/S0002-9947-2010-05049-4

Received by editor(s):
September 12, 2008

Received by editor(s) in revised form:
February 26, 2009

Published electronically:
August 25, 2010

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.