Semiconjugate Rational Functions: A Dynamical Approach

F. Pakovich

doi:10.1007/s40598-018-0081-6

Semiconjugate Rational Functions: A Dynamical Approach

F. Pakovich

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

Using dynamical methods we give a new proof of the theorem saying that if A, B, X are rational functions of complex variable z of degree at least two such that A∘ X= X∘ B and C(B, X) = C(z) , then the Galois closure of the field extension C(z) / C(X) has genus zero or one.

Original language	American English
Pages (from-to)	59-68
Number of pages	10
Journal	Arnold Mathematical Journal
Volume	4
Issue number	1
DOIs	https://doi.org/10.1007/s40598-018-0081-6
State	Published - 1 Apr 2018

Keywords

Galois closure
Invariant curves
Orbifolds
Poincaré functions
Semiconjugate rational functions

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s40598-018-0081-6

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title = "Semiconjugate Rational Functions: A Dynamical Approach",

abstract = "Using dynamical methods we give a new proof of the theorem saying that if A, B, X are rational functions of complex variable z of degree at least two such that A∘ X= X∘ B and C(B, X) = C(z) , then the Galois closure of the field extension C(z) / C(X) has genus zero or one.",

keywords = "Galois closure, Invariant curves, Orbifolds, Poincar{\'e} functions, Semiconjugate rational functions",

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AB - Using dynamical methods we give a new proof of the theorem saying that if A, B, X are rational functions of complex variable z of degree at least two such that A∘ X= X∘ B and C(B, X) = C(z) , then the Galois closure of the field extension C(z) / C(X) has genus zero or one.

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KW - Invariant curves

KW - Orbifolds

KW - Poincaré functions

KW - Semiconjugate rational functions

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Semiconjugate Rational Functions: A Dynamical Approach

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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