Ergodic Transformations in the Space of p‐Adic Integers

  title={Ergodic Transformations in the Space of p‐Adic Integers},
  author={Vladimir Anashin},
  journal={arXiv: Dynamical Systems},
  • V. Anashin
  • Published 5 February 2006
  • Mathematics
  • arXiv: Dynamical Systems
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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