Polycyclic groups of diffeomorphisms of the closed interval (Q1028091)

In this short note, the author describes a contrast between the groups of diffeomorphisms of the half-open interval and those of the closed interval. He gives a classification of the polycyclic groups of orientation-preserving \(C^2\)-diffeomorphisms of the closed interval. This shows that many polycyclic groups of the \(C^2\)-diffeomorphisms of the half-open interval are not the restriction of groups of \(C^2\)-diffeomorphisms of the closed interval.