TY - JOUR

T1 - On semiconjugate rational functions

AU - Pakovich, Fedor

N1 - Publisher Copyright:
© 2016, Springer International Publishing.

PY - 2016/7/1

Y1 - 2016/7/1

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.

UR - http://www.scopus.com/inward/record.url?scp=84988568894&partnerID=8YFLogxK

U2 - 10.1007/s00039-016-0383-6

DO - 10.1007/s00039-016-0383-6

M3 - Article

AN - SCOPUS:84988568894

VL - 26

SP - 1217

EP - 1243

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 4

ER -