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Commuting finite Blaschke products

Published online by Cambridge University Press:  01 June 1999

CARLOS ARTEAGA
CARLOS ARTEAGA
Affiliation:
Departamento de Matematica - ICEX, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, 30161-970, Belo Horizonte-MG, Brazil
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Abstract

We consider the set of finite Blaschke products $F$ for which the fixed points on the circle $S^1$ are expanding and we prove that if $F'(x) \ne F'(y)$ for all different fixed points $x,y$ of $F$ on $S^1$, then $F$ commutes only with its own powers.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 3 , June 1999 , pp. 549 - 552
Copyright
1999 Cambridge University Press

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