Two Works on Iteration and Related Questions

I want to give a brief account of results which have been communicated to me and which have been obtained by two young geometers, Eri Jabotinsky and Michel Liintz. Mr. Liintz is unhappily in a concentration camp in France. I must add that this is one of the reasons for the fact, for which I must apologize, that I am writing this exposé only now, although I have had both works in my possession for several months. The impossibility of communicating with Mr. Liintz and therefore of asking him for any explanation made the examination of his paper especially difficult. As is well known, the problem of iteration, a function f(x) being given, consists in finding a one-parameter family of functions fn(x) —f{n,x) such that, for n = 1, we have (1) ƒ(!, *) = ƒ(*) and, moreover, for any mt n, (2) fm[fn{x)] =ƒ,»+„(*); also (3) M oc) = x which follows from (2) as is seen by taking m = 0. The question is connected with Abel's functional equation