Ergodic functions over Fq[[T]]

In this paper, we present some sufficient and necessary conditions for a 1-Lipschitz function over Fq[[T]] to be ergodic, and constructions of ergodic functions over Fq[[T]], thus generalize the existing results of the case q=2, which are parallel to the pioneering work of Anashin and others, in the case of Z2. We describe the ergodic functions only in terms of Van der Put basis, which might be good enough for application considerations.