DYNAMICS OF THE p-ADIC SHIFT AND APPLICATIONS

There is a natural continuous realization of the one-sided Bernoulli shift on the p-adic integers as the map that shifts the coefficients of the p-adic expansion to the left. We study this map's Mahler power series expansion. We prove strong results on p-adic valuations of the coefficients in this expansion, and show that certain natural maps (including many polynomials) are in a sense small perturbations of the shift. As a result, these polynomials share the shift map's important dynamical properties. This provides a novel approach to an earlier result of the authors.