  An (asynchronous) automaton transformation of one-sided infinite words over
p-letter alphabet Fp = Z/pZ, where p is a prime, is a continuous transformation
(w.r.t. the p-adic metric) of the ring of p-adic integers Zp. Moreover, an
automaton mapping generates a non-Archimedean dynamical system on Zp.
Measure-preservation and ergodicity (w.r.t. the Haar measure) of such dynamical
systems play an important role in cryptography (e.g., in stream cyphers). The
aim of this paper is to present a novel way of realizing a complex shift in
p-adics. In particular, we introduce conditions on the Mahler expansion of a
transformation on the p-adics which are sufficient for it to be complex shift.
Moreover, we have a sufficient condition of ergodicity of such mappings in
terms of Mahler expansion.
