On iteration groups of certain functions. (English) Zbl 0721.39002

Neuman, František

Arch. Math., Brno 25, No. 4, 185-194 (1989).

Let I be an open interval of \({\mathbb{R}}\), n a positive integer, and G an iteration group of \(C^ n\)-diffeomorphisms of I into I. Moreover, suppose that graphs of different elements of G do not intersect each other. A characterization theorem is given for groups formed, up to conjugacy, by certain functions of the form \(\arctan (a \tan t+b)/(c \tan t+d)\) with \(a,b,c,d\in {\mathbb{R}}\) and \(| ad-bc| =1\).

Reviewer: B.Ebanks (Louisville)

MSC:

39B12	Iteration theory, iterative and composite equations
39B52	Functional equations for functions with more general domains and/or ranges

Keywords:

iteration group; diffeomorphisms; characterization theorem