# Ergodic Transformations in the Space of p‐Adic Integers

@article{Anashin2006ErgodicTI, title={Ergodic Transformations in the Space of p‐Adic Integers}, author={Vladimir Anashin}, journal={arXiv: Dynamical Systems}, year={2006}, volume={826}, pages={3-24} }

Let L1 be the set of all mappings f : Zp → Zp of the space of all p‐adic integers Zp into itself that satisfy Lipschitz condition with a constant 1. We prove that the mapping f ∈ L1 is ergodic with respect to the normalized Haar measure on Zp if and only if f induces a single cycle permutation on each residue ring Z/pkZ modulo pk, for all k = 1, 2, 3, …. The multivariate case, as well as measure‐preserving mappings, are considered also.Results of the paper in a combination with earlier results…

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