Ergodic Uniformly Differentiable Functions Modulo p on ℤp

Ergodicity for uniformly differentiable modulo $p$ functions on ${\mathbb Z}_p$

“…Memić et al [21] provided necessary and sufficient conditions for a uniformly differentiable modulo p, 1-Lipschitz function on Z p to be ergodic in terms of the van der Put coefficients. We revisit their criterion for ergodicity and give an complete description of ergodicity for a uniformly differentiable modulo p, 1-Lipschitz function on Z p in terms of the coefficients of Mahler and van der Put.…”

“…We revisit their criterion for ergodicity and give an complete description of ergodicity for a uniformly differentiable modulo p, 1-Lipschitz function on Z p in terms of the coefficients of Mahler and van der Put. We first recall the ergodicity criterion of Memić et al [21], which can be rephrased in a slightly different form.…”

“…He then raised an open question of finding necessary and sufficient conditions for uniformly differentiable modulo p functions on Z p to be ergodic. As a partial answer to this question, Memić et al [21] gave an ergodicity criterion for such functions in terms of intrinsic data associated with the given function (see Theorem 4.8). Along this line of research, Jeong [14] gave necessary and sufficient conditions for ergodic 1-Lipschitz functions of B-class in expansions of Mahler and van der Put.…”

Mahler coefficients of a certain class of compatible functions on $\mathbb{Z}_{p}$

“…Specific classes of functions are described in terms of their Mahler coefficients in many papers [4,2,3,5,6,7,8]. In this work we study the class of compatible functions satisfying the congruence (3.1) below.…”