Extending local analytic conjugacies

Inou, Hiroyuki

doi:10.1090/S0002-9947-2010-05049-4

Extending local analytic conjugacies
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by Hiroyuki Inou PDF

Trans. Amer. Math. Soc. 363 (2011), 331-343 Request permission

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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