In this talk, we present an ergodicity criterion of a certain class of 1-Lipschitz functions on $$extract_itex$$\mathbb{Z}_p$$/extract_itex$$ for arbitrary primes $$extract_itex$$p,$$/extract_itex$$ known as $$extract_itex$$\mathcal{B}$$/extract_itex$$-functions. These functions are locally analytic functions of order 1 (and therefore contain polynomials). For arbitrary primes $$extract_itex$$p\geq 5,$$/extract_itex$$ this erodicity criterion leads to an efficient and practical method of constructing ergodic polynomials on $$extract_itex$$\Z_p$$/extract_itex$$ that realize a given unicyclic permutation modulo $$extract_itex$$p.$$/extract_itex$$ In particular, for polynomials over $$extract_itex$$\mathbb{Z}_3$$/extract_itex$$, we provide a complete ergodicity criterion in terms of its coefficients. This method can be applied to a $$extract_itex$$\mathbb{Z}_p$$/extract_itex$$ for general primes $$extract_itex$$p.$$/extract_itex$$