IJPAM: Volume 34, No. 1 (2007)

FUNCTIONS COMMUTING WITH ITERATION GROUPS

Krzysztof Cieplinski
Institute of Mathematics
Pedagogical University
Podchorazych 2, Kraków, 30-084, POLAND
e-mail: kc@ap.krakow.pl


Abstract.We prove that if ${\cal F}=\{f^{t}:I \longrightarrow I ,\:\: t\in \r \}$ is a suitable iteration group on an open interval $I$ and a continuous at least at one point function $g:I\longrightarrow I$ commutes with two mappings $f^{a},\: f^{b}\in {\cal F}$ such that $\frac{b}{a}$ is irrational, then $g\in {\cal F}$.

Received: October 17, 2006

AMS Subject Classification: 39B12

Key Words and Phrases: commuting functions, (strictly disjoint) iteration group

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 1