Criteria for the stability of p-linear maps and p-powers

Iterated integral p-linear maps and p-powers arise in the theory of representations of nonlinear systems. In studies by the author (1989) necessary and sufficient conditions were given for such operators to be stable in a standard sense, and it was shown that a well-known sufficient condition is not necessary for all p>or=2, and corresponding results for discrete-time cases were given. These results are reviewed in the paper.<>