Invariants of a class of transformation groups II.
This paper shows a simple construction of continuous involutions of real intervals in terms of continuous even functions. We also study smooth involutions defined by symmetric equations. Finally, we review some applications, in particular a characterization of isochronous potentials by means of smooth involutions.
We work with a fixed N-tuple of quasi-arithmetic means generated by an N-tuple of continuous monotone functions (I an interval) satisfying certain regularity conditions. It is known [initially Gauss, later Gustin, Borwein, Toader, Lehmer, Schoenberg, Foster, Philips et al.] that the iterations of the mapping tend pointwise to a mapping having values on the diagonal of . Each of [all equal] coordinates of the limit is a new mean, called the Gaussian product of the means taken on b. We effectively...