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

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

8 Scopus citations

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	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

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s40598-018-0081-6

Cite this

@article{beeae4c2f090466c937ca12e95a0ebe1,

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",

author = "F. Pakovich",

note = "Publisher Copyright: {\textcopyright} 2018, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.",

year = "2018",

month = apr,

day = "1",

doi = "10.1007/s40598-018-0081-6",

language = "English",

volume = "4",

pages = "59--68",

journal = "Arnold Mathematical Journal",

issn = "2199-6792",

publisher = "Springer International Publishing AG",

number = "1",

}

TY - JOUR

T1 - Semiconjugate Rational Functions

T2 - A Dynamical Approach

AU - Pakovich, F.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - 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.

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.

KW - Galois closure

KW - Invariant curves

KW - Orbifolds

KW - Poincaré functions

KW - Semiconjugate rational functions

UR - http://www.scopus.com/inward/record.url?scp=85041896409&partnerID=8YFLogxK

U2 - 10.1007/s40598-018-0081-6

DO - 10.1007/s40598-018-0081-6

M3 - Article

AN - SCOPUS:85041896409

SN - 2199-6792

VL - 4

SP - 59

EP - 68

JO - Arnold Mathematical Journal

JF - Arnold Mathematical Journal

IS - 1

ER -

Semiconjugate Rational Functions: A Dynamical Approach

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this