Commuting functions and simultaneous Abel equations
Volume 60 / 1994
Annales Polonici Mathematici 60 (1994), 119-135
DOI: 10.4064/ap-60-2-119-135
Abstract
The system of Abel equations α(f_t(x)) = α(x) + λ(t), t ∈ T, is studied under the general assumption that $f_t$ are pairwise commuting homeomorphisms of a real interval and have no fixed points (T is an arbitrary non-empty set). A result concerning embeddability of rational iteration groups in continuous groups is proved as a simple consequence of the obtained theorems.
