On semiconjugate rational functions

Fedor Pakovich

doi:10.1007/s00039-016-0383-6

On semiconjugate rational functions

Fedor Pakovich

Department of Mathematics

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

17 Scopus citations

Abstract

We investigate semiconjugate rational functions, that is rational functions A, B related by the functional equation A∘ X= X∘ B, where X is a rational function. We show that if A and B is a pair of such functions, then either A can be obtained from B by a certain iterative process, or A and B can be described in terms of orbifolds of non-negative Euler characteristic on the Riemann sphere.

Original language	English
Pages (from-to)	1217-1243
Number of pages	27
Journal	Geometric and Functional Analysis
Volume	26
Issue number	4
DOIs	https://doi.org/10.1007/s00039-016-0383-6
State	Published - 1 Jul 2016

ASJC Scopus subject areas

Analysis
Geometry and Topology

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title = "On semiconjugate rational functions",

abstract = "We investigate semiconjugate rational functions, that is rational functions A, B related by the functional equation A∘ X= X∘ B, where X is a rational function. We show that if A and B is a pair of such functions, then either A can be obtained from B by a certain iterative process, or A and B can be described in terms of orbifolds of non-negative Euler characteristic on the Riemann sphere.",

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N2 - We investigate semiconjugate rational functions, that is rational functions A, B related by the functional equation A∘ X= X∘ B, where X is a rational function. We show that if A and B is a pair of such functions, then either A can be obtained from B by a certain iterative process, or A and B can be described in terms of orbifolds of non-negative Euler characteristic on the Riemann sphere.

AB - We investigate semiconjugate rational functions, that is rational functions A, B related by the functional equation A∘ X= X∘ B, where X is a rational function. We show that if A and B is a pair of such functions, then either A can be obtained from B by a certain iterative process, or A and B can be described in terms of orbifolds of non-negative Euler characteristic on the Riemann sphere.

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U2 - 10.1007/s00039-016-0383-6

DO - 10.1007/s00039-016-0383-6

M3 - Article

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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

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On semiconjugate rational functions

Abstract

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