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Abstract <p> We define a representation of isometric functions on the ring of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic integers <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb{Z}_{p}\)</EquationSource> </InlineEquation> in terms of permutations of the set <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\{0,\ldots, p-1\}.\)</EquationSource> </InlineEquation> We also provide new ergodicity criteria using these representations. </p>

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On a Representation of Isometric Transformations on \(\mathbb{Z}_{p}\) and Some Applications

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Nacima Memić,
  • Amil Pečenković

摘要

Abstract

We define a representation of isometric functions on the ring of \(p\) -adic integers \(\mathbb{Z}_{p}\) in terms of permutations of the set \(\{0,\ldots, p-1\}.\) We also provide new ergodicity criteria using these representations.