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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.