Extending local analytic conjugacies
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- by Hiroyuki Inou
- Trans. Amer. Math. Soc. 363 (2011), 331-343
- DOI: https://doi.org/10.1090/S0002-9947-2010-05049-4
- Published electronically: August 25, 2010
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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.References
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Bibliographic Information
- Hiroyuki Inou
- Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
- MR Author ID: 673749
- ORCID: 0000-0001-5613-7987
- Received by editor(s): September 12, 2008
- Received by editor(s) in revised form: February 26, 2009
- Published electronically: August 25, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 331-343
- MSC (2010): Primary 37F10; Secondary 32B10, 30D05
- DOI: https://doi.org/10.1090/S0002-9947-2010-05049-4
- MathSciNet review: 2719684