Toward the ergodicity of p-adic 1-Lipschitz functions represented by the van der Put series

Yurova (2010) [17] and Anashin et al. (2011 [3], preprint [4]) characterize the ergodicity of a 1-Lipschitz function on Z2Z2 in terms of the van der Put expansion. Motivated by their recent work, we provide the sufficient conditions for the ergodicity of such a function defined on a more general setting ZpZp. In addition, we provide alternative proofs of two criteria (because of Anashin et al., 2011 [3], preprint [4] and Yurova, 2010 [17]) for an ergodic 1-Lipschitz function on Z2Z2, represented by both the Mahler basis and the van der Put basis.