  This paper discusses a general method for spectral type theorems using metric
spaces instead of vector spaces. Advantages of this approach are that it
applies to genuinely non-linear situations and also to random versions. Metric
analogs of operator norm, spectral radius, eigenvalue, linear functional, and
weak convergence are suggested. Applications explained include generalizations
of the mean ergodic theorem, the Wolff-Denjoy theorem and Thurston's spectral
theorem for surface homeomorphisms.
