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 Z(2) in terms of the van der Put expansion. Motivated by their recent mirk, we provide the sufficient conditions for the ergodicity of such a function defined on a more general setting Z(p). 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 Z(2), represented by both the Mahler basis and the van der Put basis. (c) 2013 Elsevier Inc. All rights reserved.