On some invariants of conjugacy of disjoint iteration groups

We give a necessary and sufficient condition for conjugacy of disjoint iteration groups of continuous functions defined on open real intervals. Moreover, we determine all homeomorphisms γ such that γ o ?^t = g ^t o γ, t ∈ R, where {?^t, t R} and {g1, t ∈ R} are given disjoint iteration groups.